Overview
- Provides applications to Markov processes, coding/information theory, population dynamics, and search engine design
- Ideal for a newly designed introductory course to probability and information theory
- Presents an engaging treatment of entropy
- Reader develops solid probabilistic intuition without the need for a course in measure theory
Part of the book series: Universitext (UTX)
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Table of contents (8 chapters)
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Front Matter
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Markov processes
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Front Matter
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Entropy and applications
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Front Matter
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Back Matter
Keywords
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.
Reviews
“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)
Authors and Affiliations
About the author
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
DOI: https://doi.org/10.1007/978-3-319-74018-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Softcover ISBN: 978-3-319-74017-1Published: 13 April 2018
eBook ISBN: 978-3-319-74018-8Published: 05 April 2018
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XVII, 220
Number of Illustrations: 3 b/w illustrations