Math 509, Stochastic Differential Equations, Fall 2003
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.