Time and location: MWF 1:00pm – 1:50pm, KAP 134.
Text: Stochastic Differential Equations: An Introduction with Applications, Sixth Edition, by Bernt Oksendal. Published by Springer (Universitext Series).
Instructor: Jianfeng Zhang, KAP 248E, (213)7409805
Email: jianfenz@usc.edu Homepage: http://almaak.usc.edu/~jianfenz
Office hours: W. 11:30-1, 2-3:30 in KAP 248 E

Course Content: 
I plan to revise the course contents as well as the presentation significantly this semester. In particular, I will add the basic materials on Backward Stochastic Differential Equations, which is closely related to standard SDEs and has been proved more and more important in applications. A tentative list of contents is as follows:
Chapter 0. Preliminaries
Chapter 1. Basics of stochastic analysis
1.1 Brownian motion
1.2 Stochastic integrals
1.3 Ito’s formula
1.4 Martingale representation theorem
1.5 Girsanov theorem
Chapter 2. Stochastic differential equations
2.1 Linear SDEs
2.2 A priori estimates for SDEs
2.3 Wellposedness of SDEs
2.4 Weak solutions of SDEs
Chapter 3. Backward SDEs
3.1 Linear BSDEs
3.2 A priori estimates of BSDEs
3.3 Wellposedness of BSDEs
Chapter 4. Decoupled Forward Backward SDEs
4.1 Markovian properties of SDEs and BSDEs
4.2 FBSDEs and PDEs
4.3 Regularity of solutions to SDEs and PDEs
4.4 Euler scheme for SDEs
4.5 Backward Euler scheme for BSDEs
Chapter 5. Additional topics and/or applications

The materials on SDEs will be from the textbook, which corresponds more or less to chapters 2-5, 7 and 8 of the book. Lectures notes will be provided for materials on BSDEs

Grading and Examination Policies 
30% of the grade will be based on homework assignments, 30% on the midterm exam, and 40% on the final exam.

Homework will be assigned in class approximately every two weeks. You are encouraged to discuss homework problems with classmates. However, you are not allowed to copy other people’s work. Solutions to homework problems can be provided upon students’ request.

The (50 minutes) midterm exam will be given in regular class time on Oct. 25, Monday. It will be open book, open notes, but noncooperative.

The final exam will be take-home, which will be handed out two weeks before the semester ends. You are not permitted to discuss the problems with others.

Feedback and Questions 
It is very useful to get feedback and questions, both inside and outside class. You are very welcome to visit me during my office hours. You can also make appointments to see me at other time.