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Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
Services
Author
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
V. Implementation tools.
VI. Basic Math II.
1. Real Variable.
2. Laws of large numbers.
3. Characteristic function.
4. Central limit theorem (CLT) II.
5. Random walk.
6. Conditional probability II.
7. Martingales and stopping times.
8. Markov process.
A. Forward and backward propagators.
B. Feller process and semi-group resolvent.
C. Forward and backward generators.
D. Forward and backward generators for Feller process.
9. Levy process.
10. Weak derivative. Fundamental solution. Calculus of distributions.
11. Functional Analysis.
12. Fourier analysis.
13. Sobolev spaces.
14. Elliptic PDE.
15. Parabolic PDE.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

Markov process.


he references for this section are [Gikhman] and [RevuzYor] .

The process $X_{t}$ in $\QTR{cal}{R}^{n}$ is a Markov process if it is self-descriptive at any time:

MATH (Markov property)
for some mapping MATH .

One may always attempt to transform a non-Markov process into a Markov process by increasing dimensionality of the process. However, it is not always possible. For example of such impossibility, think of a diffusion process with volatility and drift components nontrivially dependent on the entire prior path.




A. Forward and backward propagators.
B. Feller process and semi-group resolvent.
C. Forward and backward generators.
D. Forward and backward generators for Feller process.

Notation. Index. Contents.


















Copyright 2007