Discrete Stochastic Processes and Applications

  • Jean-François Collet

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

Introduction

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.

Keywords

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

  • Jean-François Collet
    • 1
  1. 1.Laboratoire J.A. DieudonnéUniversité de Nice Sophia-AntipolisNice Cedex 02France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-74018-8
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-74017-1
  • Online ISBN 978-3-319-74018-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book