Time and location: MWF 1:00pm – 1:50pm, KAP 113.
Text: Stochastic Differential Equations: An Introduction with Applications, Fifth Edition, by Bernt Oksendal. Published by Springer (Universitext Series).
Instructor: Jianfeng Zhang, DRB 354, (213)7409805
Email: jianfenz@usc.edu Homepage: http://math.usc.edu/~jianfenz
Office hours: M: 12:00-1:00 (DRB 354), W: 11:00-12:00 (DRB 354), F: 12:00-1:00 (MC)
Course Content:
Brownian motion, stochastic integration, Ito’s formula, existence and uniqueness theorems for stochastic differential equations, diffusion processes, Feynman-Kac formula, Girsanov transformation. This corresponds more or less to chapters 2-5, 7 and 8 of the text.
The rest of the course will deal with some applications. Possible topics include connections with elliptic linear partial differential equations (chapter 9) and option pricing theory(chapter 12). The particular choice of material will depend on the interests of the students taking the course.
Grading and Examination Policies
40% of the grade will be based on homework assignments, 20% will be based on the midterm exam, and 40% will be based on the final exam.
Homework will be assigned in class approximately every two weeks. You are permitted and even encouraged to discuss homework problems with classmates. However, you are not permitted to look at what a classmate will actually submit.
The (one hour) midterm exam will be given in regular class time on Oct. 17, Friday. It will be open book, open notes, but noncooperative.
The final exam will be a take-home exam, 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.