MTH 550   Probability and Stochastic Processes

Instructor: Lubos Thoma
Office: Tyler Hall 214
Email: thoma@math.uri.edu
Tel: 874.4451
Class schedule: MW 4.30 - 5.45pm, Ballentine 102
Office hours: MW 3.00--4.00pm, F 1.00--2.00pm

Homework: Homework set 1 Homework set 2 Homework set 3 Homework set 4 Homework set 5 Homework set 6

References, additional reading: References on branching processes References on random walks A paper on the median in the gamma distribution.

Links: a depository of current preprints in probability Probability Theory and Related Fields (Springer) Electronic Journal in Probability a list of probability journals Random Structures & Algorithms

Simulations: Matlab functions for simulation of random variables and many random processes are available here (including branching processes). Maple worksheet simulating a random walk and an example output of it. Maple worksheet simulating a two-dimensional random walk. Simulations of one-dimensional and two-dimensional random walks written in java. More simulation and description of random walks: 1d random walk, 2d random walk, and self-awoiding random walk.

Syllabus:   postscript

Description:   This is a graduate class in probability theory and random processes for students in mathematics, engineering, finance, and computer science. Prerequisites are MTH 451 (Probability) or an equivalent course, linear algebra, and some advanced calculus. 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.

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

Additional texts:
      N. Alon, J. Spencer, The Probabilistic Method, Wiley-Interscience, 2000.
      I. Sinai, Probability Theory: An Introductory Course, Springer-Verlag, 1992.