Essentials of Stochastic Processes, 3rd Edition

Authors: Richard Durrett



A concise treatment and textbook on the most important topics in Stochastic Processes

All concepts illustrated by examples and more than 300 carefully chosen exercises for effective learning

New edition includes added and revised exercises, including many biological exercises, in addition to restructured and rewritten sections with a goal toward clarity and simplicity

Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding.

Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded.  In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.

Table of contents

Front Matter
Pages i-ix

Markov Chains
Pages 1-94

Poisson Processes
Pages 95-124

Renewal Processes
Pages 125-145

Continuous Time Markov Chains
Pages 147-200

Martingales
Pages 201-222

Mathematical Finance
Pages 223-250

Back Matter
Pages 251-275