Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities
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I. Basic math.
II. Pricing and Hedging.
III. Explicit techniques.
IV. Data Analysis.
1. Time Series.
A. Time series forecasting.
B. Updating a linear forecast.
C. Kalman filter I.
D. Kalman filter II.
a. General Kalman filter problem.
b. General Kalman filter solution.
c. Convolution of normal distributions.
d. Kalman filter calculation for linear model.
e. Kalman filter in non-linear situation.
f. Unscented transformation.
E. Simultaneous equations.
2. Classical statistics.
3. Bayesian statistics.
V. Implementation tools.
VI. Basic Math II.
VII. Implementation tools II.
VIII. Bibliography
Notation. Index. Contents.

General Kalman filter problem.

e consider the scheme

MATH (Kalman II model)
where the functions $A,B$ are known and smooth. The $x_{t}$ is observable. The $\xi_{t}$ is not observable. The $w_{t}$ and $v_{t}$ are Gaussian noise, determined at time $t$ . We denote MATH . We are given the initial distribution MATH , MATH Prob MATH . We would like to determine the distributions MATH , $t=1,...$ as the information $X_{t}$ becomes available.

Notation. Index. Contents.

Copyright 2007