MAP 4102 PROBABILITY THEORY AND STOCHASTIC PROCESSES 2 - SPRING 2003

Instructor: Z.R. Pop-Stojanovic

Office: Little Hall 496

Phone: 392-0281 ext. 260

E-mail: zps@math.ufl.edu

Office hours: Mondays, Wednesdays, and Fridays 10:30 a.m. - 11:30 a.m., and by appointments.

This course is intended as a first course in Stochastic Processes for upper undergraduate and beginning graduate students. Normally, such a course requires students's familiarity with the following two areas: (i)Advanced Calculus; (ii) The first course in the Probability Theory (without Measure Theory).

After an introduction which will re-introduce the concepts of random variable, the expectation, the conditional expectation, basic convergence theorems, Borel-Cantelli lemma, Kolmogorov 0-1 law, the course will present discrete Markov chains - recurrence and transience, random walks, birth and death chains, the ruin problem and branching processes - and their stationary distributions.

The next topic will deal with continuous parameter Markov chains - Poisson process, queues, birth and death chains, stationary distributions. The course will end with a treatment of spatial processes, such as the Percolation process and the continuous parameter Branching Random Walk.

Textbook: CLASSICAL AND SPATIAL STOCHASTIC PROCESSES, by Rinaldo B. Schinazi, Birkhauzer, Boston, 1999, ISBN 0-8176-4081-9.

Note: Some topics may be presented in different ways from those presented in the textbook. Taking lecture notes is a necessity for success in this course.

Tests: There are three tests given on the following days: February 07, March 14, and April 18. Each of these tests carries 24 points. In addition, there is the final test given as scheduled. It carries 48 points.

Grading scale: let S be the total sum of all test scores. A: S at least 108; B: S at least 96; C: S below 96.

Teaching format: The course will be offered in 2+1 format, that is, in two weekly lectures followed by a problem solving session.

Homework: After each lecture, a set of exercises will be assigned. These exercises will be worked out and discussed in problem solving sessions. Your participation in these sessions is expected.