© 2018

Discrete Stochastic Processes and Applications


Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Markov processes

    1. Front Matter
      Pages 1-1
    2. Jean-François Collet
      Pages 3-32
    3. Jean-François Collet
      Pages 33-55
    4. Jean-François Collet
      Pages 57-73
    5. Jean-François Collet
      Pages 75-101
    6. Jean-François Collet
      Pages 103-117
  3. Entropy and applications

    1. Front Matter
      Pages 119-119
    2. Jean-François Collet
      Pages 121-138
    3. Jean-François Collet
      Pages 139-160
    4. Jean-François Collet
      Pages 161-170
  4. Back Matter
    Pages 171-220

About this book


This unique text for beginning graduate students gives a self-contained introduction to the mathematical properties of stochastics and presents their applications to Markov processes, coding theory, population dynamics, and search engine design. The book is ideal for a newly designed course in an introduction to probability and information theory. Prerequisites include working knowledge of linear algebra, calculus, and probability theory. The first part of the text focuses on the rigorous theory of Markov processes on countable spaces (Markov chains) and provides the basis to developing solid probabilistic intuition without the need for a course in measure theory. The approach taken is gradual beginning with the case of discrete time and moving on to that of continuous time. The second part of this text is more applied; its core introduces various uses of convexity in probability and presents a nice treatment of entropy.


Markov processes Brownian motion Perron-Frobenius theorem Poisson process information theory search engine design Markov chains probability information theory graduate textbook adoption coding theory probability applications population dynamics entropy

Authors and affiliations

  1. 1.Laboratoire J.A. DieudonnéUniversité de Nice Sophia-AntipolisNice Cedex 02France

About the authors

Jean-François Collet received his PhD from the University of Bloomington in 1992 and has been Maître de Conférences at the Laboratoire J.A. Dieudonné, Université de Nice Sophia-Antipolis since 1993. Professor Collet’s research interests include Partial Differential Equations and Information theory.

Bibliographic information

  • Book Title Discrete Stochastic Processes and Applications
  • Authors Jean-François Collet
  • Series Title Universitext
  • Series Abbreviated Title Universitext
  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-74017-1
  • eBook ISBN 978-3-319-74018-8
  • Series ISSN 0172-5939
  • Series E-ISSN 2191-6675
  • Edition Number 1
  • Number of Pages XVII, 220
  • Number of Illustrations 3 b/w illustrations, 0 illustrations in colour
  • Topics Probability Theory and Stochastic Processes
  • Buy this book on publisher's site
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“This textbook is a very nice introductory material to the subjects of discrete and continuous-time Markov chains, and information theory with applications to binary coding. It is nicely written and it provides a self-contained treatment of the topics.” (Nikola Sandrić, zbMATH 1431.60001, 2020)

“The ideal audience for this text would be students or practitioners in that sweet spot where mathematical rigor is important … . an excellent reference for Markov Chain theory for an instructor struggling to determine how much rigor to introduce into a course on Markov chains.” (John K. McSweeney, MAA Reviews, September 22, 2019)