Description:   This is a graduate class in probability theory and random processes for students in mathematics, engineering, finance, and computer science. The purpose of the course is to present the basic concepts and techniques of probability theory as well as some of their applications. Emphasis will be placed on fundamental principles, thinking probabilistically, and methods and results of modern probability theory.

Topics will include: basic properties of probability measures, discrete and continuous random variables, distributions, random walks, generating functions, limit theorems, large deviations, Markov chains and Markov processes, branching processes, Poisson processes, martingales, Brownian motion. To illustrate the general theory the class will include many applications (taking into account interests of the audience) to mathematics (e.g. discrete mathematics, percolations), engineering (e.g. signal processing), computer science (e.g. analysis of random(ized) algorithms), and mathematical finance.

Syllabus, lecture notes, and homework:     Please login into sakai at URI

Textbook:     G. Grimmett and D. Stirzaker, Probability and Random Processes, Oxford University Press, third edition, 0-19-857222-0.

Additional texts:
      A. Gut: Probability, A graduate course, Springer Verlag 2005
      G. Lawler: Introduction to Stochastic Processes, CRC Press 2006
      I. Sinai, Probability Theory: An Introductory Course, Springer-Verlag, 1992

Prerequisites: (MTH435 or MTH437) and MTH451

Accommodations: Any student with a documented disability is welcome to contact me as early in the semester as possible so that we may arrange reasonable accommodations. As part of this process, please be in touch with Disability Services for Students Office at 330 Memorial Union, 401-874-2098.