Stochastic Processes

Stochastic Differential Equations

Math 565C
Spring 2021
Times/Place Mondays, Wednesdays 8:00 - 9:15am (we may change this if everyone agrees); in ENR2 390 (third floor bubble)

Instructor: Sunder Sethuraman
Office: ENR2 S413
Telephone: (520) 621-1774
E-Mail: sethuram@math.arizona.edu
- Although there is no required text, we will follow mostly introductory books by L.C. Evans, and Oksendal (both available in e-form from the library).
- The following, among others, though will be useful in parts of the course:
  - Introduction to Random Processes, NV Krylov
  - Stochastic Processes, R Bass
  - Continuous Time Markov Processes (AMS), TM Liggett
  - Stochastic Processes (Courant Lectures), SRS Varadhan
  - Probability: Theory and Examples, R. Durrett
  - Stochastic Calculus (CRC), R. Durrett
  - BM and Stochastic Calculus, Karatzas-Shreve (Springer)
  - Continuous Time Martingales and BM, Revuz-Yor (Springer)
  - Markov Processes: Characterization and Convergence (Wiley), T. Kurtz
  - Diffusions, Markov Processes and Martingales, Rogers-Williams
  - Stochastic Differential Equations, Bhattacharya, Waymire
  - Stochastic Integration and Differential Equations, Protter
  - Foundations of Modern Probability, O. Kallenberg
- The lecture notes of J. Watkins for a similar course in 2006 may be useful as a resource. There are also other lecture notes on this subject available on the web.
- Syllabus/Tentative Schedule: We will begin with some preliminary material on what a SDE is, and Brownian motion. Then, we will proceed to define stochastic integrals with respect to BM, and other processes. We will also cover `stochastic differential equations' and Ito calculus, as well as connections to solution of certain PDE, among other things. Depending on class interests, we may study an example of an SPDE or an application near the end of the course.
- Grades will be based on the HW's, every 2 weeks or so.