Office Hours: TR 12:45 - 1:30 and 4:30-5:15. Also by
appointment.
Class Hours: TR 2:00 - 3:15
Text:
There will be no unique textbook for this course. We start with the last chapters of
Probability Essentials. Authors: Jean Jacod and Philip Protter, Springer; 2nd Edition.
and continue with
Probability: Theory and Examples. Author:
Richard Durrett, Duxbury Press; Fifth Edition.
Additional reading:
- Continuous time Markov processes : an introduction
Author: Thomas M.
Liggett.
AMS Graduate studies in mathematics, v. 113.
QA274.7 .L54 2010;
ISBN : 9780821849491.
-
Stochastic Processes (Courant Lecture Notes)
Author: S.R.S. Varadhan
ISBN-13: 978-0821840856.
- Additional references will be added as we progress through the material.
Grading policy: Based on homework assigned about every two weeks plus a take home final exam. Description:
MTH722 - Probability theory II - Stochastic Processes - is
a continuation of MTH721 (Probability Theory I), a measure theoretical introduction to probability theory. Topics: Conditional expectation, Martingales, Discrete and continuous time Markov processes, Dynkin-Feller processes, Brownian motion and introduction to Ito
processes and Ito Calculus.
Prerequisites:
The course is as self contained as possible.
MTH 721. Undergraduate background: MTH224, 524/624, 533-534.
MTH 712, 725, 730-631 are helpful but not mandatory.