Discrete Stochastic Processes and Applications

ISBN-13: 9783319740171 / Angielski / Miękka / 2018 / 220 str.

Jean-Francois Collet

Opis

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.

Recenzje

"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 Sandric, 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)

Spis treści

Preface.- I. Markov processes.- 1. Discrete time, countable space.- 2. Linear algebra and search engines.- 3. The Poisson process.- 4. Continuous time, discrete space.- 5. Examples.- II. Entropy and applications.- 6. Prelude: a user's guide to convexity.- 7. The basic quantities of information theory.- 8. An example of application: binary coding.- A. Some useful facts from calculus.- B. Some useful facts from probability.- C. Some useful facts from linear algebra.- D. An arithmetical lemma.- E. Table of exponential families.- References.- Index.

O autorze

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.

Blurb

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.