Discrete Stochastic Processes and Applicat...

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

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

Inhaltsverzeichnis

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.

Erscheinungsjahr:	2018
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Universitext
Inhalt:	xvii 220 S. 3 s/w Illustr. 220 p. 3 illus.
ISBN-13:	9783319740171
ISBN-10:	3319740172
Sprache:	Englisch
Herstellernummer:	978-3-319-74017-1
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Collet, Jean-François
Auflage:	1st ed. 2018
Hersteller:	Springer International Publishing Springer International Publishing AG Universitext
Maße:	235 x 155 x 14 mm
Von/Mit:	Jean-François Collet
Erscheinungsdatum:	13.04.2018
Gewicht:	0,371 kg

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