MATH 697U: Stochastic Processes and Applications, Spring 2020

Meeting : TuTh 11:30--12:45    LGRT 173

Instructor : Luc Rey-Bellet

Office :  1423 K LGRT
Phone :  545-6020
E-Mail : luc <at> math.umass.edu
Office Hours :   Tu 3:00-4:00,   W 10:00--12:00,   or by appointment.

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Classnotes:


Text: The textbook for the class is the book by Bremaud . There are however many other excellent texts.
The book by Lawler is an excellent and very efficient introductory textbook which will cover a large part of the class. It is highly recommended for a first read to have a broad overview.
The book by Sheldon Ross is a more elementary one. It has a lot of very good examples. I used part of chapter 11 on simulation to prepare for my class.
The books by Resnick and Durrett are more advanced and are recommended for the more mathematically oriented student.
The books by Madras and Rubinstein-Kroese are about Monte-Carlo methods and Simulation.
The book by Levin, Peres and Wilmer is a great book about the modern theory of finite state Markov chains. I am using part of the first four chapters of the book for our class.

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Syllabus: This course is an introduction to stochastic processes and Monte-Carlo methods. Prerequisite are a good working knowledge of calculus and elementary probability as in Stat 607, or Stat 605. And we will use from time to time some concepts from analysis and linear algebra. One of the main goal in the class is to develop a "probabilist intuition and way of thinking". We will present some proofs and we will skip some others in order to provide a reasonably broad range of topics, concepts and techniques. We emphasize examples both in discrete and continuous time from a wide range of disciplines, for example branching processes, queueing systems, population models, chemical reaction networks and so on. We will also discuss the numerical implementation of Markov chains and discuss the basics of Monte-Carlo algorithms. Among the topics treated in the class are

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