Instructor: Xia Chen

Office: Ayres 241, 974-4284.

Email: xchen@math.utk.edu

Website: http://www.math.utk.edu/~xchen

Class: MWF 10:10a.m.-11a.m. (Ayress 114)

Office Hours: MWF 2:00-3:00pm.

** Textbook:**

Brownian motion--
an introduction to stochastic processes
By Rene L. Schilling and Lothar Partzsch (2012).

**Reference Books: **

Continuous martingales and Brownian motion. By Daniel Revuz and Marc Yor
(1991)

**Course Description:**

As the single 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. Its central rule in mathematics is also matched by
numerous applications in science, engineering and mathematical finance.
This course aims to provide a systematic account for the sample properties
of Brownian motions. If the situation allowed, we will continue on the
same topic in Spring, 2018 (Math 624).

**Grading policy:**

There will be no test and exams. Your
performance in the classroom and in homework will decide the grade you receive.

**Prerequisite:**

Officially, it requires
Math523-524 (probability at graduate level) or equivalent.
If you are not sure whether or not this course is right for you,
please stop by and discuss it with me

**Homework #1 **

Chapter 1: 5. Chapter 2: 5, 8, 13, 19, 21, 23.

**Homework #1 solution **
(pdf)

**Homework #2 **

Chapter 3: 2. Chapter 5: 4, 6, 10, 11, 17, 18, 19.

**Homework #2 solution **
(pdf)

**Homework #3 **

Chapter 6: 1, 5, 6, 8, 11, 12.

**Homework #3 solution **
(pdf)

**Homework #4 **

Chapter 7: 3, 6, 9, 10, 13, 18.
Chapter 8: 2, 4, 5.

**Homework #4 solution **
(pdf)

**Homework #5 **

Chapter 9: 5, 6. Chapter 10: 1, 5.
Chapter 12: 2, 3. Chapter 14:
(Suplemental problems)

**Homework #5 solution **
(pdf).
Chapter 19: 3, 5, 9, 10, 14.