An Introduction to Markov Processes: 230 (Graduate Texts in Mathematics) - Softcover

Stroock, Daniel W. W.

Softcover

ISBN 10: 3662517825 ISBN 13: 9783662517826

Verlag: Springer, 2016

Inhaltsangabe

<P>THIS BOOK PROVIDES A RIGOROUS BUT ELEMENTARY INTRODUCTION TO THE THEORY OF MARKOV PROCESSES ON A COUNTABLE STATE SPACE. IT SHOULD BE ACCESSIBLE TO STUDENTS WITH A SOLID UNDERGRADUATE BACKGROUND IN MATHEMATICS, INCLUDING STUDENTS FROM ENGINEERING, ECONOMICS, PHYSICS, AND BIOLOGY. TOPICS COVERED ARE: DOEBLIN'S THEORY, GENERAL ERGODIC PROPERTIES, AND CONTINUOUS TIME PROCESSES. APPLICATIONS ARE DISPERSED THROUGHOUT THE BOOK. IN ADDITION, A WHOLE CHAPTER IS DEVOTED TO REVERSIBLE PROCESSES AND THE USE OF THEIR ASSOCIATED DIRICHLET FORMS TO ESTIMATE THE RATE OF CONVERGENCE TO EQUILIBRIUM. THESE RESULTS ARE THEN APPLIED TO THE ANALYSIS OF THE METROPOLIS (A.K.A SIMULATED ANNEALING) ALGORITHM.</P><P>THE CORRECTED AND ENLARGED 2<SUP>ND</SUP> EDITION CONTAINS A NEW CHAPTER IN WHICH THE AUTHOR DEVELOPS COMPUTATIONAL METHODS FOR MARKOV CHAINS ON A FINITE STATE SPACE. MOST INTRIGUING IS THE SECTION WITH A NEW TECHNIQUE FOR COMPUTING STATIONARY MEASURES, WHICH IS APPLIED TO DERIVATIONS OF WILSON'S ALGORITHM AND KIRCHOFF'S FORMULA FOR SPANNING TREES IN A CONNECTED GRAPH.</P>

Über diesen Titel

Reseña del editor

This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. Topics covered include: Doeblin's theory, general ergodic properties, and continuous time processes.

Contraportada

This book provides a rigorous but elementary introduction to the theory of Markov Processes on a countable state space. It should be accessible to students with a solid undergraduate background in mathematics, including students from engineering, economics, physics, and biology. Topics covered are: Doeblin's theory, general ergodic properties, and continuous time processes. Applications are dispersed throughout the book. In addition, a whole chapter is devoted to reversible processes and the use of their associated Dirichlet forms to estimate the rate of convergence to equilibrium. These results are then applied to the analysis of the Metropolis (a.k.a simulated annealing) algorithm.

The corrected and enlarged 2nd edition contains a new chapter in which the author develops computational methods for Markov chains on a finite state space. Most intriguing is the section with a new technique for computing stationary measures, which is applied to derivations of Wilson's algorithm and Kirchoff's formula for spanning trees in a connected graph.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2016
• ISBN 10: 3662517825
• ISBN 13: 9783662517826
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 224