Nicolas Privault: Understanding Markov Chains

Cover: 9789811306587 | Understanding Markov Chains | Examples and Applications | Privault

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Sprache: Englisch

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Beschreibung

This book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.

Über den Autor

The author is an associate professor from the Nanyang Technological University (NTU) and is well-established in the field of stochastic processes and a highly respected probabilist. He has authored the book, Stochastic Analysis in Discrete and Continuous Settings: With Normal Martingales, Lecture Notes in Mathematics, Springer, 2009 and was a co-editor for the book, Stochastic Analysis with Financial Applications, Progress in Probability, Vol. 65, Springer Basel, 2011. Aside from these two Springer titles, he has authored several others. He is currently teaching the course M27004-Probability Theory and Stochastic Processes at NTU. The manuscript has been developed over the years from his courses on Stochastic Processes.

Zusammenfassung

Easily accessible to both mathematics and non-mathematics majors who are taking an introductory course on Stochastic Processes

Filled with numerous exercises to test students' understanding of key concepts

A gentle introduction to help students ease into later chapters, also suitable for self-study

Accompanied with computer simulation codes in R and Python

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Inhaltsverzeichnis

Probability Background.- Gambling Problems.- Random Walks.- Discrete-Time Markov Chains.- First Step Analysis.- Classification of States.- Long-Run Behavior of Markov Chains.- Branching Processes.- Continuous-Time Markov Chains.- Discrete-Time Martingales.- Spatial Poisson Processes.- Reliability Theory.

Details

Erscheinungsjahr:	2018
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Springer Undergraduate Mathematics Series
Inhalt:	xvii 372 S. 44 s/w Illustr. 372 p. 44 illus.
ISBN-13:	9789811306587
ISBN-10:	9811306583
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Privault, Nicolas
Auflage:	2nd ed. 2018
Hersteller:	Springer Singapore Springer Nature Singapore Springer Undergraduate Mathematics Series
Maße:	235 x 155 x 22 mm
Von/Mit:	Nicolas Privault
Erscheinungsdatum:	15.08.2018
Gewicht:	0,593 kg

Artikel-ID: 113592783