Information Page, Math 236 "Introduction to Stochastic Differential Equations." Winter 2022

Course Description:

This is an introductory graduate course in Stochastic Differential Equations (SDE). Prerequisites for the course are basic probability at the level of Math 136. Some basic knowledge of partial differential equations is needed for a more rounded understanding of SDE. Prerequisites are not enforced. Each person can decide for themselves if they have a suitable background preparation for the class, and discuss this with the instructor. The lectures are mostly self-contained and someone willing to devote some extra study time can make up for missing background material.

Instructor:

Name	Office	Office Hours	email
George Papanicolaou	380-383V	Tuesdays 3:00-5:00pm and by appointment or email	papanicolaou at stanford dot edu

CA:

Name	Office Hours	email
Simona Diaconu	TBD	sdiaconu at stanford dot edu

Textbook

The textbook for the course is "Stochastic Differential Equations ", Sixth Edition, by Brent Oksendal. It should be in the bookstore. We will cover Chapters 1-5 approximately. I will NOT use the rest of the book.

Lecture notes for this course are available in the homework section.

The following books are recommended for background reading or for special topics: G. Grimmett and D. Stirzaker, Probability and Random Processes; L. Breiman, Probability; J.L. Doob, Stochastic Processes; R. Durrett, The essentials of probability; R. Durrett, Stochastic Calculus; L. Breiman, Probability and Stochastic Processes, an Introduction; W. Strauss, Introduction to Partial Differential Equations; L.C. Evans, Partial Differential Equations. Also recommended for a more complete treatment of SDE: I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, Second Edition.

Grading Policy

There will be a take-home final exam given out on Friday March 4. It is due on Friday March 18 at 5 pm. Grades are due on March 22. The take-home exam will count for 60 percent of the grade. The homeworks will count for 40 percent of the grade. I will give homework sets roughly every other week, beginning on January 7 and they will be due one week later. The CA will grade the homeworks. We will provide solutions to the homework problems one week after they are assigned.