Syllabus for Math 562, Section E1
## Fall 2008, CRN 33567

## Theory of
Probability, II

Roughly, this is a course about stochastic differential equations and
the associated ideas of Ito calculus. We hope to understand both of these
subjects and understand some of their structure. By structure, we mean
some different perspectives and applications which reveal different perspectives
on the material. Our goal will be to present this knowledge in a way which
will be accessible to engineers who possess a certain level of mathematical
maturity and at the same time to be precise enough that the mathematics
student should have little trouble filling in the details. While Math
561 is not a prerequisite, you should be willing to dig through the
notes for that class (which are online) to fill in as much detail as you
need. Similarly, while you are not required per se to know measure theory,
you should be able to become comfortable with the usage of measure theory
(I will give a brief summary of the relevant portions of measure theory
as needed).

## Provisional Schedule

- Lecture 0: A scenic trip through measure theory
- Lecture 1: Brownian motion
- Review of Brownian motion
- Scaling properties

- Lecture 2: Stochastic integration and differentiation
- Lecture 3: Stochastic differential equations
- Lecture 4: Markov processes
- Lecture 5: Asymptotics

**Grading**: Grades will
be determined on the basis of homework (30%), a midterm (30%) and a
final (40%).

**Text**: Øksendal, Stochastic Differential Equations, Springer-Verlag, 6th ed., 2003

**Additional Reference: **Karatzas and Shreve, Brownian Motion and Stochastic Calculus, Springer-Verlag

**Instructor:** Richard Sowers

**Office:** 347 Illini Hall

**Phone:** (217) 333-6246

**email:** r-sowers@illinois.edu

**Home page:** https://math.uiuc.edu/~r-sowers

**Class meets:** MWF 1-2 in 447 Altgeld Hall

**Office Hours:** MW 11:30-1