AMATH 572: Introduction to Applied Stochastic Analysis

SLN 10232, MW 3:30-4:50, Loew Hall 115
(Prerequisites: )


Professor Hong Qian
Lewis 319
tel: 543-2584
fax: 685-1440
office hours: M,W 12:00-1PM

Homework Grades 2010 Web Page

Course description Textbook Syllabus Objectives Schedule

Course Description

Introduction to the theory of probability and stochasitc processes based on differential equations with applications to science and engineering. Poisson processes and continuous-time Markov processes, Brownian motions and diffusion. Prerequisite: AMATH/STAT 506, AMATH 402, or equivalent knowledge of probability and ordinary differential equations. Offered: Sp.


Gardiner, Crispin Stochastic Methods: A Handbook for the Natural and Social Sciences (4th Ed., Springer Series in Synergetics, 2009) Available at the University Bookstore.


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), biology and life science, 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.

Reading Materials

0. A historical account by E.W. Montroll

1. Dynamics based on distributions: A new perspective

2. Review on probability and random variables

3. Markov processes (part 1)

3. Markov processes (part 2)

4. Markov processes with continuous time and state space: Kolmogorov forward differential equation

5. Markov jump processes with discrete state space and continuous time

6. Poisson process and master equations

7. Birth-death processes and nonlinear population dynamics

8. On properties of statistical estimators

9. Brownian motion

7. Stochastic differential equation

Schedule and Homework

Homework and Exams Homework Due Date Homework Problem Sets Homework Solutions
First day of classes Monday, March 31
Homework#1 due Monday, April 14 Homework #1
Homework#2 due Monday, April 21 Homework #2
Homework#3 due Monday, April 28 Homework #3
Homework#4 due Monday, May 5 Homework #4
Homework#5 due Monday, May 12 Homework #5
Homework#6 due Monday, May 19 Homework #6
Homework#7 due Monday, June 2 Homework #7
Memorial Day Monday, May 26 No class
Term Paper Due Friday, June 6



<> Mon Mar 8 15:19:14 PST 2010