Instructor: Xia Chen
Office: Ayres 318, 974-4284.
Email: xchen3@tennessee.edu
Website: http://www.math.utk.edu/~xchen
Class: TR 11:20am-12:35pm. (Ayress G004)
Office Hours: TR 10:00 a.m.- 11:00 a.m.
Textbook: Brownian motion-- a guide to random processes and stochastic calculus. By Rene L. Schilling (2021) (3rd edition)
Reference Books:
Continuous martingales and Brownian motion. By Daniel Revuz and Marc Yor (1991)
Brownian motion. By Yuval Peres and Peter Morters (2010)
Course Description:
As the most important stochastic process, Brownian motion appears as
intersection of three fundamental classes of processes: It is a martingale, a
Gaussian process and a Markov process. Since observed by physicists,
Brownian motion has been in the center of the investigation
for both mathematicians and the people
in many other disciplines. Its fascinating link to the partial differential
equations and harmonic analysis symbols the modern day of probability.
As the scaling limit of the random walks,
Brownian motion serves a bridge between analysis and some hard problems
of discrete structure.
The course is the continuation of Math 623 of the last semester. The main
forcus in this semester is Ito-calculus (driven by Brownian motions)
and the realated topics. The Chapters we plan to cover (with
possible adjustment) are Chpter 15, 16, 17,
18, 19, 21, and 23.
Grading policy:
There will be no test and exams. Your
performance in the classroom and in homework will decide the grade you receive.
Homework #1 Due: Feb. 13 (Tuesday)
Chapter 15: 5, 8, 12, 13, 16, 17, 18
Solution to Homework #1 (pdf)
Homework #2 Due: March 5 (Tuesday)
Chapter 18: 1, 6, 9, 10, 14, 16
Solution to Homework #2 (pdf)
Homework #3 Due: April 30 (Tuesday)
Chapter 19: 2, 3, 4, 5, 6. Chapter 20: 2, 5, 6,
13 (a, b).
Homework #4
Chapter 21: 5, 14.