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I. Wavelet calculations.
II. Calculation of approximation spaces in one dimension.
III. Calculation of approximation spaces in one dimension II.
IV. One dimensional problems.
1. Decomposition of payoff function in one dimension. Adaptive multiscaled approximation.
2. Constructing wavelet basis with Dirichlet boundary conditions.
3. Accelerated calculation of Gram matrix.
4. Adapting wavelet basis to arbitrary interval.
5. Solving one dimensional elliptic PDEs.
6. Discontinuous Galerkin technique II.
A. Rebalancing wavelet basis.
B. Reduction to system of linear algebraic equations.
7. Solving one dimensional Black PDE.
8. Solving one dimensional mean reverting equation.
V. Stochastic optimization in one dimension.
VI. Scalar product in N-dimensions.
VII. Wavelet transform of payoff function in N-dimensions.
VIII. Solving N-dimensional PDEs.
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Discontinuous Galerkin technique II.


e continue where we left off in the section ( Discretization for backward Kolmogorov equation ).




A. Rebalancing wavelet basis.
B. Reduction to system of linear algebraic equations.

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