Syllabus for Math 562

• Instructor: Renming Song
• Office: 338 Illini Hall
• Phone: (217) 244 6604
• email: rsong at math uiuc edu
• Home page: http://www.math.uiuc.edu/~rsong
• Office Hours: MWF 1:00-1:50 P. M. or by appointment
• Class Hours: MWF 2:00-2:50 P.M.
• Classroom: 243 Altgeld Hall

References: 1. D. Revuz and M. Yor: Continuous martingales and Brownian motion (3rd edition), Springer, 1999; 2. I. Karatzas and S. E. Shreve: Brownian motion and stochastic calculus (2nd edition), Springer, 1991; 3. S. E. Shreve: Stochastic calculus for finance I and II, Springer, 2004

Course Topics This is the second half of the basic graduate course in probability theory. The goal of this course is to understand the basic theory of stochastic calculus. We will cover the following topics: (1) Brownian motion; (2) continuous time matingales; (3) Markov processes; (4) stochastic integrals; (5) Ito's formula; (6) representation of martingales; (7) Girsanov theorem and (8) stochastic differential equations. If time allows, we will give a brief introduction to mathematical finance. The prerequisite for Math 562 is Math 561..

Grading Policy 50% of your grade will depend on homework assignment, and 50% will depend on a final exam.