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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
1. Calculational Linear Algebra.
2. Wavelet Analysis.
A. Elementary definitions of wavelet analysis.
B. Haar functions.
C. Multiresolution analysis.
D. Orthonormal wavelet bases.
a. Auxiliary function of OST.
b. Scaling equation for wavelet.
c. Existence of orthonormal wavelet bases.
E. Discrete wavelet transform.
F. Construction of MRA from scaling filter or auxiliary function.
G. Consequences and conditions for vanishing moments of wavelets.
H. Existence of smooth compactly supported wavelets. Daubechies polynomials.
I. Semi-orthogonal wavelet bases.
J. Construction of (G)MRA and wavelets on an interval.
3. Finite element method.
4. Construction of approximation spaces.
5. Time discretization.
6. Variational inequalities.
VIII. Bibliography
Notation. Index. Contents.

Orthonormal wavelet bases.


n this section we utilize the concept of MRA to provide a recipe for construction of orthonormal wavelet basis, see the definition ( Orthonormal wavelet basis ).

Notation

(Notation W_d) Given a function MATH we introduce the notation MATH




a. Auxiliary function of OST.
b. Scaling equation for wavelet.
c. Existence of orthonormal wavelet bases.

Notation. Index. Contents.


















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