**Instructor:**Renming Song**Office:**338 Illini Hall**Phone:**(217) 244 6604**email:**rsong at illinois dot edu**Home page:**`https://faculty.illinois.edu/~rsong`

**Class Hours:**MWF 9 am--9:50 am**Classroom:**447 Altgeld Hall**Office Hours:**MWF 1 pm -1:50 pm

**Text:** Jean-Francois Le Gall:
Brownian Motion, Martingales, and Stochastic Calculus
Springer, 2016.

** Course Topics:**
This is the second half of the basic graduate course in probability
theory. This course will concentrate on stochastic calculus and
its applications. In particular, we will cover, among other things,
the following topics: Brownian motion, stochastic integrals, Ito's formula,
martingale representation theorem, Girsanov's theorem, stochastic
differential equations, connections to partial differential equations.
If there is interest from the audience and if time allows, we
will also cover applications to mathematical finance.

Math 561 is a prerequisite for this course. However, if you have not taken Math 561, but are willing to invest some extra time to pick up the necessary materials from 561, you may register for this course.

** Grading Policy:**
Your grade will depend on
homework assignment and a possible final exam.