STOCHASTIC PROCESSES

This book contains material on compound Poisson random variables including an identity which can be used to efficiently compute moments, Poisson approximations, and coverage of the mean time spent in transient states as well as examples relating to the Gibb's sampler, the Metropolis algorithm and mean cover time in star graphs.

Table of Contents:

1. Preliminaries.

2. The Poisson Process.

3. Renewal Theory.

4. Markov Chains.

5. Continuous-Time Markov Chains.

6. Martingales.

7. Random Walks.

8. Brownian Motion and Other Markov Processes.

9. Stochastic Order Relations.

10. Poisson Approximations.

Answers and Solutions to Selected Problems.