Index.

Quantitative Analysis

Parallel Processing

Numerical Analysis

C++ Multithreading

Python for Excel

Python Utilities

Printable PDF file

I.

II.

Pricing and Hedging.

III.

Explicit techniques.

IV.

V.

Implementation tools.

VI.

VII.

Implementation tools II.

VIII.

Index.

1-dimensional Lagrange element

2-dimensional Lagrange element

A priory estimate for penalised solution 1

A priory estimates for Galerkin solution 1

AS convergence vs convergence in pr 1

AS convergence vs convergence in pr 2

Accelerated calculation of Gram matrix

Adapting GMRA to interval [0,1] section

Adapting MRA to the interval [0,1] section

Adapting dual wavelets to interval [0,1] section

Adapting scaling function to the interval [0,1] section

Adapting wavelet basis to arbitrary interval

Adapting wavelets to the interval [0,1] section

Adaptive approximation section

Adaptive time step for Black PDE section

Adjoint of surjection

Adjustment of scale

Affine alpha component

Affine beta component

Affine boundary conditions

Affine characteristic function 1

Affine characteristic function 2

Affine_equation_ab

Affine_equation_section

Algebraic tensor product of Hilbert spaces

Almost sure convergence

Almost sure convergence 2

AlphaK and BetaK 1

AlphaK and BetaK 2

Alternating_boundary

Alternating_boundary1

Alternating_boundary2

Alternating_directions1

Alternating_directions2

Analytic preconditioner for Black equation

Analytical preconditioner derived from asymptotic decomposition in time

Analytical solution for mean reverting equation

Approximate toy problem

Approximation and detail operators

Approximation and detail operators 2

Approximation and detail operators 3

Approximation and detail operators 4

Approximation and detail operators section

Approximation by smooth functions

Approximation in Nitsche norm

Arzela-Ascoli compactness criterion

Assumption of coercivity 1

Asymptotic expansion for Black equation section

Asymptotic expansion of Laplace integral

Asymptotic expansion of Laplace integral section

Asymptotic expansions chapter

Asymptotic of generic Laplace integral

Asymptotic of integral with Gaussian kernel

AvellanedaLawrence

Average difference lemma

Averaged Taylor polynomial

Averaged Taylor polynomial section

Backward Euler convergence 2

Backward Euler problem

Backward Kolmogorov PDE

Backward Kolmogorov PDE setup

Backward Kolmogorov equation

Backward Kolmogorov for Feller process

Backward Kolmogorov for discounted payoff

Backward Kolmogorov for running payoff

Backward Kolmogorov generator

Backward Kolmogorov with localization

Backward Kolmogorov with running payoff

Backward discontinuous Galerkin time-discretization

Backward induction

Backward propagator

Backward_equation_for_jump_diffusion

Backward_equation_section

Banach fixed point theorem

Basic Math II part

Basic coherence condition

Basic existence of incomplete market pricing

Basic existence result

Basic properties of Fourier transform

Basic properties of conditional expectation

Basic properties of propagator 1

Basic properties of propagator 2

Basic property of orthogonal polynomials

Basis in Hilbert space

Basket credt derivative section

Bayesian_technique

Baysian_statistics_section

Bellman equation section

Bernstein inequality for wavelets

Bessel equality

BetaK separation of random walk

Bilinear form B

Bilinear form B 2

Biorthogonal QMF conditions

Biorthogonal QMF property 1

Biorthogonal QMF property 2

Biorthogonal scaling functions

Biorthogonal symmetry 1

Biorthogonal symmetry 2

Biorthogonal symmetry 3

Biorthogonality

Biorthogonality criteria 1

Black Scholes formula

Black Scholes property 1

Black final payoff plot

Black solution plot

BlackScholesUndiscountedCall

Borel measurable function

Borell-Cantelli's lemma, part 1

Borell-Cantelli's lemma, part 2

Boundary elliptic regularity

Boundedness of adjoint of surjection

Boundedness of interpolation operator

Boundedness of surjection

Bounds of interpolation error section

Box-Muller procedure

Bramble-Hilbert lemma

Brownian_motion

C to W1p estimate

C0gamma vs W1p estimate

Calculation of approximation spaces chapter

Calculation of approximation spaces in one dimension. Take two.

Calculation of biorthogonal wavelets section

Calculation of boundary scaling functions

Calculation of boundary scaling functions section

Calculation of boundary wavelets

Calculation of partial sums

Calculation of partial sums in parallel section

Calculation of scalar product in N dim

Calculation of scaling functions section

Calculation of w1 for a positive section

Calculation of w2 for a positive section

Calculation of w3 for a positive section

Calculational Linear Algebra chapter

Calculus behind the PiecewisePoly project section

Calculus behind the poly module section

Caratheodory theorem

Caratheodory theorem remark figure

Cascade algorithm

Cauchy inequality

Cauchy inequality for scalar product 1

Cauchy inequality for scalar product 2

Cauchy inequality for scalar product section

Cauchy inequality with epsilon

Central limit theorem

Central limit theorem (CLT) II section

Cg to W1p estimate

Change of numeraire kernel

Change_of_Brownian_motion

Change_of_drift_recipe

Change_of_drift_recipe_1

Change_of_measure_definition_section

Change_of_measure_recipe_section

Change_of_numeraire_definition_section

Change_of_numeraire_recipe_section

Changing scale of wavelet basis

Characterisation of H-tilde spaces

Characteristic exponent of a pm

Characteristic function chapter

Characteristic measure of Poisson point process

Chebyshev inequality

Chebyshev polynomials

Chebyshev polynomials calculation

Chebyshev polynomials orthogonality

Chebyshev polynomials section

Chf of entrance time 1

Chi squared distribution section

Choice of interval

Choosing probing functions section

Chunkiness parameter

Closedness and recession figure

Closeness and lower semicontinuity

Coefficients of quadrature rule

Coherent measure

Common shape identification

Common_application_of_change_of_measure

Compactly supported scaling function

Compactly supported smooth biorthogonal wavelets section

Complementary slackness

Complete measure space

Complete normed space

Complete tensor product of Hilbert spaces

Completion of measure via addition of null sets

Condition number

Conditional expectation

Conditional probability chapter

Conditionally_independent_defaults

Conjugate directions

Conjugate duality theorem

Conjugate gradient residue selection

Conjugate gradients

Connection between SLA and minimization

Constant finite element

Constraint qualification 1

Constraint qualification 2

Constraint qualification 3

Constraint qualification 4

Constraint qualification 5

Constructing dual GMRA on 01 with boundary conditions section

Constructing maximum summary

Construction of MRA and wavelets on half line or an interval section

Construction of MRA section

Construction of approximation spaces section

Construction of generic Levy process

Construction of symmetric biorthogonal wavelets

Continuity lemma

Continuity point

Convergence in Lp and in probability 1

Convergence in Lp and in probability 2

Convergence lemma for family of complex numbers

Convergence of cascade procedure section

Convergence of conjugate gradient method

Convergence of discontinuous Galerkin technique

Convergence of finite elements for generic parabolic operator section

Convergence of modified cascade procedure section

Convergence of pm and chf 1

Convergence of pm and chf 2

Convergence of product

Convergence theorem for martingales

Conversion of representations

Convex Hull Cone Relative Interior

Convex and proper function

Convex function picture

Convex homogenous function property

Convexity of partial minimum

Convolution and smoothing section

Convolution of polynomials 1

Convolution of polynomials 2

Convolution of polynomials 3

Convolution of polynomials 4

Copula_calculation_for_CDO

Corrected difference 2 figure

Corrected difference figure

Crank-Nicolson convergence for heat equation

Crank-Nicolson problem for heat equation

Credit risk figure 1

Credit risk figure 2

Credit risk figure 3

Credit_default_swap_section

Criteria of positive definiteness

Crossing points figure 1

Crossing points figure 2

Crossing points figure 3

Crossing theorem 1

Crossing theorem 2

Crossing theorem 2 figure

Crudification of piecewise-quadratic representation

Crudification operator

Crudification operator 2

Cuda and python section

Currency exchange section

Currency_change_of_numeraire_recipe

Cutoff function

DHE with term structure

Data Analysis part

Decomposition of a convex set

Decomposition of payoff function in one dimension section

Definition of A_i

Definition of Epsilon

Definition of Galerkin basis 1

Definition of K0

Definition of K1

Definition of P_i

Definition of Q_i

Definition of conditional probability section

Definition of g_k

Definition of the Poisson process

Definition_of_change_of_measure

Definitions and the main convergence theorem section

Delta_hedging_with_predictable_jump_section

Derivative vs scale

Deterministic optimal control problem section

Diagonal preconditioner section

Difference figure

Differential inequality 1

Differential inequality 2

Differentiating call with respect to maturity 1

Differentiating call with respect to maturity 2

Differentiation of asymptotic power series

Dimension mismatch

Dimension of tensor product

Dirac delta function

Direct Fourier transform

Direction of recession figure

Directional derivative

Directions of recession

Dirichlet problem for generic parabolic operator

Discontinuous Galerkin time-discretization

Discrete wavelet transform section

Discrete wavelet transform setup

Discretization for backward Kolmogorov equation section

Discretization with respect to time parameter section

Displaced Heston equations

Displaced Heston equations chapter

Displaced diffusion section

Dissipation property of Feller process

Distribution density via Call

Distribution of Poisson process section

Dominated convergence theorem

Dual Sobolev spaces section

Dual feasibility

Dual wavelets properties

Dual wavelets section

Duality gap and geometric multipliers

Duality picture 1

Duality picture 2

Eigenfunctions of Laplacian

Eigenvalues of compact symmetric operator

Eigenvalues of symmetric elliptic operator

Elementary definitions of wavelet analysis section

Elliptic Dirichlet problem

Elliptic PDE section

Elliptic Ritz projection

Elliptic alternative 1

Elliptic alternative 2

Elliptic boundedness of inverse

Elliptic differential operator

Elliptic regularity for Poisson equation

Elliptic regularity section

Embedding of dual Sobolev space

Energy approximation

Energy estimate 2

Energy estimates for the Galerkin approximate solution

Energy estimates for the bilinear form B

Equivalence of AS and PR convergence for series

Equivalence of toy problems

Equivalent definitions of vague convergence

Equivalent sequences of rv

Error and residual

Error and residual 2

Estimate for K0

Estimate for K1 one

Estimate for K1 two

Estimate of interpolation error

Estimate of interpolation error 2

Estimate of interpolation error 3

Estimate of mean by probability series

Estimation of averaged Taylor polynomial

Euler Lagrange equation

Evaluating matrix R section

Eventuality of random walk

Evolution figure

Evolution with penalty term

Evolution_equation

Evolutionary penalised problem

Evolutionary variational inequalities section

Evolutionary variational inequality problem

Example Black equation parameters section

Example Black problem

Example approximate problem

Example stochastic elliptic problem

Example strong Black problem

Example strong Black problem 2

Example strong elliptic problem

Example weak elliptic problem

Existence and uniqueness for evolutionary problem

Existence and uniqueness for non-coercive stationary problem.

Existence and uniqueness for penalised problem

Existence and uniqueness for penalised problem 2

Existence and uniqueness for stationary problem

Existence for Galerkin approximation of stationary problem

Existence of Lagrange multipliers for equality constraints

Existence of Lebesgue measure

Existence of adapted wavelets

Existence of biorthogonal basis 1

Existence of biorthogonal compactly supported wavelets

Existence of conditional expectation

Existence of derivative via finite difference

Existence of incomplete market pricing

Existence of orthogonal polynomials

Existence of orthonormal wavelet bases 1

Existence of orthonormal wavelet bases 2

Existence of smooth compactly supported wavelets

Existence of subdifferential

Existence of wavelets with orthogonality across scales

Existence of weak solution for elliptic Dirichlet problem 1

Existence of weak solution for elliptic Dirichlet problem 2

Existence of weak solution for elliptic Dirichlet problem 3

Existence of weak solution for the parabolic Dirichlet problem

Existence of weak solution of the Heat equation

Existence of weak solution of the Poisson equation

Explicit_scheme

Exponential change

Extension of Borell-Cantelli lemma to random walk

Extension of measure to sigma algebra

Extension theorem

Extremal properties of orthogonal polynomials

Extreme points of polyhedral set 1

Extreme points of polyhedral set 2

Fair Variance vs Log contract

Feasible direction cone

Feller process property 1

Filtration_definition_section

Finite QMF convergence

Finite difference basics

Finite difference basics section

Finite difference in Sobolev space

Finite difference schemes for heat equation section

Finite differences

Finite dimensional approximation 1

Finite dimensional approximation 2

Finite element section

Finite elements chapter

Finite elements for Poisson equation with Dirichlet boundary conditions section

Finite space variable incomplete market

First order PDE

Form of Schwarz operator

Forward Kolmogorov equation for Ito process

Forward and backward generators def

Forward and backward generators section

Forward propagator

Forward_Kolmogorov

Forward_exchange_rate

Fourier analysis in Hilbert space section

Fourier decomposition

Fourier series on unit interval

Fourier series section

Fourier transform

Fourier transform of convolution

Fourier transform of delta function section

Fourier transform of projection on span of translates

Fourier transform section

Frame formula 1

Frame property 1

Frame property 2

Frame property 3

Fredholm alternative

Free boundary problem 1

Free boundary problem 2

Free boundary problem 2 summary

Friedrich lemma

Fritz John conditions

Function spaces section

Functional analysis chapter

Fundamental solution for ODE

GMRA Ries bases

Gagliardo-Nirenberg-Sobolev inequality

Galerkin approximation 1

Galerkin approximation 2

Galerkin approximation for parabolic Dirichlet problem section

Galerkin approximation of stationary problem

Galerkin coefficients

Galerkin convergence 1

Galerkin convergence 2

Galerkin convergence 3

Galerkin convergence 4

Galerkin convergence 5

Galerkin convergence 6

Galerkin problem

Gamma function primer

Gamma_distribution

Gauss-Hermite Intergration

Gaussian quadrature rule

General_change_of_Brownian_motion

Generalized multiresolution analysis

Generator of Levy process

Generic Backward Kolmogorov

Generic Forward Kolmogorov

Generic parabolic PDE

Generic parabolic PDE problem

Generic parabolic PDE setup

Geometric multiplier

Geometric multiplier property

Gershgorin circle theorem

Girsanov theorem

Girsanov_kernel

Girsanov_theorem

Girsanov_theorem_A

Global approximation by smooth functions

Gram-Schmidt orthogonalization section

Gyongy lemma section

Haar functions section

Hahn decomposition theorem

Hankel determinants

Heat equation weak formulation 1

Heat equation weak formulation 2

Heat equation with Dirichlet boundary condition

Heat equation with Neumann boundary condition

Heston approximation

Heston_equation_section

Heston_equations

Hewitt and Savage zero-or-one law

High order internal elliptic regularity

Higher degree of exactness

Holder inequality

Holder inequality 2

Holder inequality 3

Holospoudic criteria

How does it extend to multiple dimensions section

Hyperplane representation

Hypothesis_testing_problem

IO criteria for AS convergence

Idea of Bayesian analysis section

Identification of nodal variables 1

Identification of nodal variables 2

Implementation for mean reverting equation section

Implementation tools II part

Implicit equation with penalty term

Implicit formulation of the penalty term section

Implicit spectrum

Implicit_scheme

Impossibility of backward induction section

Improving condition number

Incomplete Market 1

Incomplete Market 2

Incomplete market ask

Incomplete market bid

Independence of Poisson processes

Independency of pre-alpha and post-alpha fields

Independent process

Induced outer measure

Infimal convex function

Infimal convolution

Infimal convolution of support functions

Infinitely divisible pm

Infinitely often zero-or-one law

Instant smoothness of solution operator for PP 1

Integral form of Taylor decomposition

Integral of scaling function

Integral of scaling function 2

Integral of wavelet

Integration by part for finite differences

Integration of fundamental solution for Black equation

Integration of polynomials

Interaction of approximation and detail operators with Fourier transform

Interaction of downsampling with Fourier transform

Interaction of tilde with Fourier transform

Interaction of upsampling with Fourier transform

Interpolated continuity

Interpolation inequality

Interpolation of Hilbert spaces section

Intersection of halfspaces

Intersection property

Inverse Fourier transform

Inversion of chf into df

Inversion of chf into pm 1

Inversion of chf into pm 2

Inversion_remark

Ito calculus section

Ito_derivative_of_product

Jackson inequality for wavelets

Jackson inequality for wavelets 2

Jensen inequality

Jordan decomposition theorem

Kalman_II_model

Kalman_filter_II_section

Known_Variance1

Known_Variance2

Kolmogorov equations in general setting

Kolmogorov inequality for series 1

Kolmogorov inequality for series 2

Kolmogorov three series theorem

Kolmogorov zero-or-one law

Kolmogorov-Chapman equation

Krank_Nicolson_spectrum

Krein-Milman theorem

Kronecker summation lemma

LIBOR market model section

Lagrange interpolation formula

Lagrange interpolation formula 1

Lagrange multiplier

Lagrangian optimality

Laplace quadrature section

Laplace transform section

Laplace_problem

Laplacian_Limits

Laplacian_Spectrum

Law of large number for iid rv with finite mean

Law of large numbers for independent rv

Lax-Milgram theorem

Lax_convergence_theorem

Lebesgue differentiation theorem

Lebesgue differentiation theorem section.

Lebesgue integral definition

Left and right derivatives

Levy process chapter

Levy-Khintchine formula 1

Levy-Khintchine formula 2

Liapounov inequality

Limsup and liminf for sets

Lindeberg-Feller CLT

Lindeberg-Feller condition

Line segment principle

Linear equation

Linear independence from biorthogonality

Linear intersection result

Linear tensor product element

Linear transformation of random variables

Local approximation by smooth functions

Local minima of convex function

Local minimum of a sum

Localised integral

Localised scaling

Localised transport

Localization for mean reverting equation section

Localization for mean reverting equation summary

Localization section

Longstaff-Schwartz technique section

Lp interpolation

Lp vs W1p estimate

Magnitude of matrix Epsilon

Main properties of direction of recession

Main property of Fourier decomposition

Main property of Haar functions 1

Main property of basis in Hilbert space

Main property of convex function

Main property of crudification operator

Main_property_of_change_of_measure

Manipulation of localized piecewise polynomial functions

Mapping of conditional expectation

MarkPr TargetEquation

MarkPr TargetEquations 2

Market model section

Market_price_of_risk

Markov property

Markovian projection

Markovian projection on displaced diffusion section

Markovian projection section

Martingale definition

Martingale property of Feller process

Mathematica Test 1

Mathematica Test 1a

Mathematica Test 2

Mathematica Test 3

Matrix of discontinuous Galerkin

Maximal dimension 1

Maximal inequality for martingales

Maximal_likelihood_section

Maximum of random walk

Mean reversion 0

Mean reversion 1

Mean reversion 2

Mean reversion 3

Mean reversion 4

Mean reversion 5

Mean reverting equation section

Mean reverting free boundary problem

Mean reverting free boundary problem 2

Mean reverting problem

Mean reverting problem 2

Mean reverting solution

Measurable space

Method of conjugate directions section

Method of conjugate gradients section

Method of steepest descent section

Min common and max crossing point section

Minimax equality

Minimax lemma 1

Minimax lemma 2

Minimax theorem

Minimax theorem 1

Minimization with equality constraints

Minimum norm optimality of Chebyshev polynomials

Minimum of a convex function

Minimum of a smooth function

Minkowski-Weyl representation

Minkowski-Weyl theorem

Mix of backward induction and penalty term approaches I. Implementation and results section

Mix of backward induction and penalty term approaches II section

Mix of backward induction and penalty term approaches section

Modified cascade procedure

Mollifier for a ball 1

Mollifier for a ball 2

Monotonicity of solution of stationary problem

Morrey inequality

Multidimensional Gyongy lemma

Multidimensional backward Kolmogorov equation

Multiplication of polynomials

Multiresolution analysis

Multiresolution analysis section

Necessary and sufficient optimality conditions

Nitsche bilinear form

Nitsche form energy estimates

No drift Black Scholes

Non emptiness of relative interior

Non-coercivity assumption 1

Nondecreasing ratio

Nonvertical separation

Nonvertical separation figure

Normal cone figure 1

Normal distribution with unknown parameters 1

Normal distribution with unknown parameters 2

Normal_variable

Numerical analysis part

One dime payoff residue figure

One dimensional problems chapter

Operations on sets and logical statements

Optimal stopping

Optimal stopping time problem section

Optimal strategy with accrual

Optimal utility section delta hedging

Optimality for smooth function figure 1

Optimality for smooth function figure 2

Optional random variable

Optional sampling theorem

Order of summation 0

Order of summation 1

Order of summation 2

Order of summation 3

Order of summation 4

Order of summation 5

Orthogonal L2 projection

Orthogonal polynomials

Orthogonal_normal_variables

Orthogonality of residues

Orthogonality of residues 2

Orthonormal system of translates def

Orthonormal system of translates section

Orthonormal wavelet bases section

Orthonormal wavelet basis

Parabolic Dirichlet problem

Parabolic PDE section

Parabolic differential operator

Parabolic problem with nonsmooth initial condition

Parabolic regularity 1

Parabolic regularity 2

Parabolic regularity for heat equation

Parabolic regularity section

Parallel subspace correction method section

Parallel subspace preconditioner

Parallel subspace preconditioner property

Parameter averaging

Parameter averaging section

Parseval equality

Partial inversion lemma

Partial inversion lemma 2

Partial minimization result

Partial solution

Partial summation in parallel

Partially inverted problem

Partially inverted semidiscrete parabolic problem

Partially inverted semidiscrete parabolic problem 1

Partition of unity definition

Pathwise differentiation

Penalisation error

Penalised evolutionary problem section

Penalized mean reverting problem

Penalized problem

Penalized problem for mean reverting equation section

Pervasive idea of recursive calculation section

PetersdorffSchwab

Piecewise Quadratic Polynomial picture

Piecewise convolution

Piecewise linear MRA section

Piecewise polynomial representation

Piecewise polynomials in parallel

Piecewise polynomials section

Pm vs chf estimate

Poincare inequality

Poincare inequality for a ball

Poisson equation weak formulation 1

Poisson equation weak formulation 2

Poisson equation with Dirichlet boundary condition

Poisson formula for delta function

Poisson formula section

Poisson point process

Poisson point process section

Poisson process chapter

Poisson property 1

Poisson property 1a

Poisson property 2

Poisson property 3

Polar cone definition

Polar cone properties

Polar cone theorem

Polar polyhedral cone

Polyhedral function

Positive definite inner product

Possible value of random walk

Post-alpha process

Pre-alpha field

Precompactness of a tight sequence of pm

Preconditioner for Black equation in case q=1 section

Preconditioning section

Preliminary reduction

Preliminary reduction 2

Preservation of closeness result

Preservation of convexity

Preservation of stationary measure

Primal feasibility

Principal intersection result

Probability based criteria for AS convergence

Projection permuation

Projection theorem

Proof of existence for stationary problem section

Propagator and transitional probability

Proper separation 1

Proper separation 2

Properties of Feller resolvent 1

Properties of Feller resolvent 2

Properties of Feller resolvent 3

Properties of Poisson point process

Properties of Schwarz operator

Properties of averaged Taylor polynomial

Properties of dual frame

Properties of frame operator

Properties of interpolant

Properties of left and right derivative

Properties of mollifiers

Properties of sequences h and g

Properties of sequences h and g section

Properties of solution operator

Properties of solution operator 2

Properties of spline functions

Properties of subgradient

Property of equivalent sequences of rv

Property of scale and transport 1

Property of scale and transport 2

Property of scale and transport 3

Property of scale and transport 4

Property of scale and transport 5

Property of scale and transport 6

Property of scale and transport 7

Property of transport 1

Property of transport 2

Pseudonormality

Python to R Communicator section

Python utilities section

Quadratic form minimum

Quadratic intersection result

Quadratic piecewise interpolation

Quadratic piecewise interpolation 2

Quadratic polynomials 1

Quadratic polynomials 2

Quadratic polynomials 3

Quadratic polynomials 4

Quadratic polynomials 5

Quadrature rule

Quadrature rule 1

Radon-Nikodym theorem

Random walk space

Random walk space approximation

Real valued random variable

Rebalancing wavelet basis problem

Rebalancing wavelet basis section

Recession cone of intersection

Recession cone of inverse image

Recovering MRA from auxilliary function 1

Recovering scaling function from auxilliary function section

Recurrence lemma 1

Recurrence lemma 2

Recurrence result 1

Recurrence result 2

Recurrent value of random walk

Recursive calculation

Recursive equation

Recursive relationships for wavelet section

Recursive relationships for wavelet transform

Reduction of Black equation

Reduction scheme 1

Reduction scheme 2

Reduction to system of linear algebraic equations for Black PDE section

Reduction to system of linear algebraic equations for mean reverting equation section

Reduction to system of linear algebraic equations for q=1

Reduction to system of linear algebraic equations for q=1 section

Reduction to system of linear algebraic equations for q=1 summary

Reduction to system of linear algebraic equations section

Reduction to system of linear algebraic equations summary

Reduction to well conditioned form section

Reflection principle picture

Reflection_principle

Regularity of a set

Relative interior figure

Rellich-Kondrachov compactness theorem

Remainder bound 1

Remainder of averaged Taylor polynomial

Remainder of averaged Taylor polynomial 2

Remainder of averaged Taylor polynomial 3

Remark on stability of financial problems

Removing stiffness from penalized equation section

Representation of dual Sobolev space

Representation of solution for elliptic PDE using stochastic process section

Reproduction of polynomials 1

Reproduction of polynomials 2

Reproduction of polynomials 3

Reproduction of polynomials 4

Resolution structure for adapted scale functions

Resolvent of Feller process

Restricted linear independence

Review of variational inequalities in maximization case section

Ricatti_equation_section

Riesz basis condition

Riesz potential bound 1

Riesz potential bound 2

Riesz representation theorem

Risk neutral Brownian motion

Risk neutral measure via Girsanov section

Risk_neutral_pricing

Ritz projection convergence 1

Saddle point defining property

Saddle point result 1

Saddle point result 2

Saddle point theorem

Same grid reduction

Saturated measure space

Scalar product in N dimensions

Scalar product in N-dimensions Test case 2

Scale and transport operators

Scale and transport operators 2

Scale of polynomial

Scaling equation

Scaling equation 2

Scaling equation 3

Scaling equation 4

Scaling equation 5

Scaling equation for wavelet section

Scaling equation section

Scaling filter and auxiliary function

Schwarz operator

Second derivative localization

Second order internal elliptic regularity

Self financing strategy

Semi-orthogonal wavelet bases section

Senior_tranche_loss

Separable and dense set

Separating hyperplane theorem

Shift and sampling operators

Shifted Fourier transform equality

Sigma finite set

Simple function definition

Simple law of large numbers

Simplistic_copula

Sklar_theorem_1

Sklar_theorem_2

Smooth compactly supported wavelets section

Smooth optimization problem

Smooth version of the penalty term section

Smoothness of compactly supported wavelets with vanishing moments

Smoothness of compactly supported wavelets with vanishing moments section

Sobolev conjugate

Sobolev inequality

Sobolev inequality 2

Sobolev space definition

Sobolev spaces in N dim as tensor products

Sobolev spaces section

Sobolev spaces with dominating mixed derivative

Solution operator for PP with nonsmooth IC

Solution operator for elliptic problem

Solution operator for generic elliptic problem

Solving N-dimensional PDEs section

Solving equation with implicit penalty term section

Solving one dimensional Black PDE section

Solving one dimensional mean reverting equation section

Space splitting setup

Sparse tensor product

Sparse tensor product approximation 1

Sparse tensor product approximation 2

Sparse tensor product definition section

Sparse tensor product section

Sparse tensor product setup

Spectral mapping theorem

Spectral_mapping

Spectrum of compact operator

Spitzer identity

Spline functions definition

Spline functions section

Stability of general evolution equation

Stability of one-dim heat equation schemes section

Stability of splitting for Sobolev spaces with dominating mixed derivative

Stability of splitting for tensor product of Sobolev spaces

Stability of wavelet splitting 1

Stability of wavelet splitting section

Stable space splittings section

Stable splitting

Standard mollifier definition

Standard_normal_variable

Star shaped set

Starting scaling function

Stationary independent increments

Stationary penalised problem

Stationary variational inequality problem

Steepest descent

Stochastic optimal control section

Stochastic optimization in one dimension chapter

Stochastic optimization over wavelet basis section

Stochastic process

Stregthened Cauchy-Schwartz inequality

Strict hyperplane separation 1

Strict hyperplane separation 2

Strong formulation of evolutionary problem

Strong formulation of stationary problem

Strong law of large numbers for iid rv

Strong law of large numbers for mean zero

Strong mean reverting problem

Strong mean reverting problem 2

Structure of recurrent values

Subgradient and subdifferential

Subprobability measure

Sufficient conditions for vanishing moments

Sufficient conditions for vanishing moments 2

Sufficient statistics for normal sample section

Sufficiently fine scale

Sufficiently fine scale 2

Suitable_numeraire

Summary for Black equation in case q=1

Summary for Black equation in case q=1 section

Summary for Black equation in case q=1, any time interval

Summary for Black equation in case q=1, inverted matrix

Summary for mean reverting equation in case q=1

Support function

Support of scaling function

Supporting hyperplane theorem

Symmetric biorthogonal wavelets section

Symmetric principal part

Symmetrization section

T-forward probability measure

Tangent cone figure 1

Tangent cone figure 2

Taylor decomposition in Peano form

Taylor decomposition in Schlomilch, Lagrange and Cauchy forms

Taylor polynomial

Tensor product of Hilbert spaces section

Tensor product of bounded operators

Tensor product of function spaces

Tensor product properties 1

Tensor product properties 2

Tensor product splitting

Three-term recurrence relation

Time dependent elliptic problem

Time dependent elliptic variational problem

Time discretization of penalty term section

Time series forecasting section

Time-weak backward Kolmogorov

Time-weak problem

Total_probability_rule

Toy approximation in energy norm

Trace-zero functions in W1p

Transformation of SDE based on delta hedging section

Transformation of SDE under change of measure

Transformation of parabolic problem 1

Transformation of parabolic problem 2

Transformation_to_heat_eq_section

Transition function

Transitive_bayes_formula

Transport of polynomial

Trigonometry primer

Two_asset_change_of_numeraire_section

Unbounded existence result

Uniform continuity of chf

Uniform convergence

Uniform property of vague convergence

Uniformly equicontinuous sequence

Uniformly smooth approximation lemma

Uniqueness of weak solution for the parabolic Dirichlet problem

Unscented conditions for mean

Unscented covariance summary

Unscented mean section

Unscented mean summary

Unscented transformation section

Unsuitability of spline wavelets

Unsuitability of spline wavelets 2

V for linear MRA 0

V for linear MRA d

V0 for linear MRA

Vague convergence

Vague convergence as a weak convergence 1

Vague convergence as a weak convergence 2

Vague convergence section

Vague precompactness of spm

Vanishing moments for biorthogonal wavelets section

Vanishing moments of wavelet section

Vanishing moments vs approximation

Vanishing moments vs approximation 2

Vanishing moments vs approximation 3

Vanishing moments vs decay at infinity

Variance of target process

Variance swap pricing section

Variational Dirichlet problem for generic parabolic operator

Variational inequalities chapter

Variational inequalities in maximization case

Variational inequality example

Variational toy problem

Visualization lemma

Wavelet analysis section

Wavelet approximation 1

Wavelet approximation 2

Wavelet approximation 3

Wavelet approximation 4

Wavelet calculations chapter

Wavelet estimates in Sobolev spaces section

Wavelets on 01 step 1

Weak backward Kolmogorov with respect to time

Weak compactness of bounded set

Weak derivative

Weak derivative section

Weak duality theorem

Weak formulation of stationary problem

Weak formulation with respect to time parameter

Weak formulation with respect to time parameter section

Weak maximal principle 1

Weak solution of elliptic Dirichlet problem

Weak solution of parabolic Dirichlet problem

Weierstrass theorem

Whittaker sampling theorem

Why_Ito_process_section

Wiener-Hopf technique

X to Y connection

Young inequality

Zeros of orthogonal polynomials

Zorn maximal principle

[0,1]-adapted GMRAs

[0,1]-adapted MRA

definition of minmax p

ess sup definition

generalized impulse equation

generalized impulse solution

log contract section

operations on sets section

recovery of implied distribution

static replication formula

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