Introduction to Applied Stochastic Analysis

!!! Notice the Room Change !!!

Course Description

Reference book

Crispin W. Gardiner Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences, (Springer Series in Synergetics , Vol 13) Springer, 1996.

Emanuel Parzen Stochastic Processes, "Classics in Applied Mathematics", SIAM, 1999 Available at the University Bookstore.

Syllabus

1. Review on random variables, Markov chains and stationary processes

2. Radioactive decay and exponetial distribution

3. Poisson processes and Gamma distributions

4. Order statistics

5. Two-state chemical kinetics and continuous-time Markov chain (Q-processes)

6. Stationarity and correlation function

7. Reversibility and entropy production

8. Kolmogorov forward and backward equations

9. Branching processes

10. Renewal processes

11. Generating function and central limit theorem

12. random walk and birth-death processes

13. Brownian motion and diffusion

14. Brownian motion with a force field

15. Kramers' proble and transition-state theory

16. Brownian motion with boundary, first passage time problem

17. Brownian motion in 2-dimension, reversibility and circulation

18. Stochastic differential equations

19. Spectral analysis of Gaussian processes

20. Strongly correlated processes

Learning Objectives and Instructor Expectations

Stochastic analysis is a new way of reasoning which has wide application in all fields of science and engineering. Different from the traditional deterministic approach, stochastic analyses try to obtain useful information from seemingly random data, and stochastic models try to develop insights into the nature of randomness. The stochastic mathematics is particularly relevant to statistical physics, (just as calculus to mechanics and linear algebra to quantum mechanics), molecular biology, nanotechnology, signal processing and communications, and many branches of science and engineering, as well as economics and finance. The course will be taught from an application standpoint with examples from many different fields.

A minimal background in probability and familiarity with differential equations are required. Homeworks are used to reinforce class lectures. Exams will emphasize basic techniques as applied to basic problems.

Coutrse Notes

The course notes (.ps, .pdf) is still being developed. So only download the necessary portion.

Schedule and Homework

Grading

Tutorials