Math/Stat 453 (Stochastic Models). Spring 2014


Instructor: Steve Krone

Office: 421 Brink Hall. Phone: 885-6317
Office Hours: by appointment.

Class Time: MWF 11:30 - 12:20
Place: AD 227

Prerequisite: Math/Stat 451 (Probability) and a strong desire to learn. Math 451 is a serious prerequisite, as is the "mathematical maturity" and sophistication necessary to know that subject at a high level. Just "getting by" in 451 will not cut it unless you are willing and able to put in the extra work needed to address any defficiencies.

Text: R. Durrett, Essentials of Stochastic Processes, 2nd ed., Springer

Grading

Homework .... 25%
Exam 1 ......... 25%
Exam 2 ......... 25%
Final .............. 25%

This is a first course in stochastic processes, the mathematics behind time-dependent random phenomena. We will introduce the main ideas and techniques from the subject and relate them to nontrivial models in science. In order to facilitate a deeper understanding, we will spend less time on the artificial examples one often finds in textbooks, and more time developing a family of related models from population genetics. This will allow us to become more intimately aware of what is going on in the models, and so make the theory more transparent with the intuition we will develop.

A rough outline of the topics is as follows:


1. Introduction

2. Discrete-Time Markov Chains and the Wright--Fisher Model

3. Martingales

4. Continuous-Time Markov Chains and the Moran Model

5. Brownian Motion and Diffusion Processes


Additional References:


Note: This course can also be taken for graduate credit as Math 538 or Stat 544. In addition to the exams and homework, students taking the graduate-level option will be expected to complete an extra reading assignment and present that material to me.