AMATH 572: Introduction to Applied Stochastic Analysis

SLN 10224, MW 3:30-4:50, Loew Hall 115
(Prerequisites: AMATH 569 which may be taken concurrently)

Instructor:

 Professor Hong Qian
Guggenheim 415E
tel: 543-2584
fax: 685-1440
qian@amath.washington.edu
office hours: TBA

Course description Textbook Syllabus Objectives Reading materials Schedule Grades

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.

Textbook

Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences by Crispin W. Gardiner (3rd Ed., Paperback, Springer Series in Synergetics, 2004)

Syllabus

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.

Reading Materials

1. A historical account by E.W. Montroll

2. Review on probability and random variables

3. Markov processes

4. Stationary, homogeneous Markov processes

5. Poisson process and master equations

6. 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 7 Homework #1 (.pdf)
Homework#2 Due Monday, April 14 Homework #2 (.pdf)
Homework#3 Due Monday, April 21 Homework #3 (.pdf)
Homework#4 Due Monday, April 28 Homework #4 (.pdf)
Homework#5 Due Mondy , May 5 Homework #5 ( .pdf)
Homework#6 Due Monday, May 12 Homework #6 (.pdf)
Memorial Day Monday, May 26 No class
Monday, June 2 No class
Wednesday, June 4 No class
Last day of classes Friday, June 6

Grading

Your course grade will be calculated by weighing your homework and term paper in the proportions 70% and 30%, respectively.