An Introduction to Stochastic Modeling


  • Mark Pinsky
  • Samuel Karlin, Stanford University and The Weizmann Institute of Science

Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, 4e, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems. New to this edition:

  • Realistic applications from a variety of disciplines integrated throughout the text, including more biological applications
  • Plentiful, completely updated problems
  • Completely updated and reorganized end-of-chapter exercise sets, 250 exercises with answers
  • New chapters of stochastic differential equations and Brownian motion and related processes
  • Additional sections on Martingale and Poisson process

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Upper division undergraduate and graduate-level courses in stochastic processes and stochastic modeling, offered in statistics and mathematics departments at all major universities.


Book information

  • Published: December 2010
  • ISBN: 978-0-12-381416-6


This book is a valuable resource for anyone studying combustion processes."
--David L. Liscinsky, United Technologist Research Center, in AIAA JOURNAL

This is an excellent text-book ... The narrative is clear, careful and detailed but, at the same time, designed to draw (not to bore) the reader in. The main strengths, in my opinion, are the wealth of convincing applications, which are discussed at some, but not too much length after each bit of theoretical development, and the large number of exercises given at the ends of sections, not just at the ends of chapters."
--Martin Crowder, University of Surrey, Guildford, in THE STATISTICIAN

Table of Contents

Conditional Probability and Conditional Expectation
Markov Chains: Introduction
The Long Run Behavior of Markov Chains
Poisson Processes
Continuous Time Markov Chains
Renewal Phenomena
Brownian Motion and Related Processes
Queueing Systems
Random Evolutions
Characteristic Functions and Their Applications