### MATH 5016: Topics in Probability

**Description:** Advanced topics in probability theory, theory of random processes, mathematical statistics, and related fields. With a change of content, this course is repeatable to a maximum of twelve credits.

**Credits:** 3

### MATH 5016 - Section 1: Jump Processes

**Description:** Researchers in many fields, such as physics, economics, finance, have realized that many real-world phenomena are better explained by models that allow for discontinuities. To give just one example, the stock market is often modeled by geometric Brownian motion, but this process doesn't allow for sudden jumps (think 9/11). I will discuss the probability theory used in studying jump processes. Topics will include Poisson processes, compound Poisson processes, Lvy processes, integro-differential operators, Poisson point processes, the stochastic calculus for jump processes, stochastic differential equations.

**Prerequisites:** The prerequisite is Math 5160, the first semester graduate probability course. I will review topics from Math 5161 as needed, so that course is not a prerequisite. There will be a few homework assignments, but no exams. The bulk of the work required is just following the lectures. There is no assigned text. I will provide references and notes as we go.

**Offered:** Fall

**Credits:** 3

**Sections: **Fall 2014 on Storrs Campus

PSCourseID | Course | Sec | Comp | Time | Room | Instructor |
---|---|---|---|---|---|---|

15023 | 5016 | 001 | Lecture | TuTh 11:00 AM-12:15 PM | MSB307 | Bass, Richard |