Basic Stochastic Processes

Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Markov chains in discrete and continuous time, renewal and regenerative processes, Poisson processes, and Brownian motion. This volume gives an in-depth description of the structure and basic properties of these stochastic processes. A main focus is on equilibrium distributions, strong laws of large numbers, and ordinary and functional central limit theorems for cost and performance parameters.

In terms of pre-requisites, the book does not demand much. Although an exposure to elementary Probability Theory would help, it is by no means es- sential. Chapter 0 is meant to supply the necessary background in Probability. The only real pre-requisite is an exposure to undergraduate Linear Algebra and Calculus, and of course, the necessary motivation. We would like to highlight one interesting feature of the present book.

This book is a collection of exercises covering all the main topics in the modern theory of stochastic processes and its applications, including finance, actuarial mathematics, queuing theory, and risk theory.