Markov Processes and Potential Theory

Name: Markov Processes and Potential Theory
Price: 12.53 USD
Availability: InStock
ISBN: 9780486462639

ISBN-10: 0486462633

ISBN-13: 9780486462639

Edition: 2007

Authors: Robert M. Blumenthal, Ronald K. Getoor

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Description:

This graduate-level text explores the relationship between Markov processes and potential theory, in addition to aspects of the theory of additive functionals. Topics include Markov processes, excessive functions, multiplicative functionals and subprocesses, and additive functionals and their potentials. A concluding chapter examines dual processes and potential theory. 1968 edition.

Book details

List price: $18.95
Copyright year: 2007
Publisher: Dover Publications, Incorporated
Publication date: 12/17/2007
Binding: Paperback
Pages: 320
Size: 5.51" wide x 8.54" long x 0.59" tall
Weight: 0.726



Preface



Preliminaries



Notation



The Monotone Class Theorem



Topological Spaces



Markov Processes



General Definitions



Transition Functions



General Definitions Continued



Equivalent Processes



The Measures P[superscript mu]



Stopping Times



Stopping Times for Markov Processes



The Strong Markov Property



Standard Processes



Measurability of Hitting Times



Further Properties of Hitting Times



Regular Step Processes



Excessive Functions



Introduction



Excessive Functions



Exceptional Sets



The Fine Topology



Alternative Characterization of Excessive Functions



Multiplicative Functionals and Subprocesses



Multiplicative Functionals



Subordinate Semigroups



Subprocesses



Resolvents and Strong Multiplicative Functionals



Excessive Functions



A Theorem of Hunt



Additive Functionals and Their Potentials



Additive Functionals



Potentials of Additive Functionals



Potentials of Continuous Additive Functionals



Potentials of Natural Additive Functionals



Classification of Excessive Functions



Further Properties of Continuous Additive Functionals



Reference Measures



Continuous Additive Functionals



Fine Supports and Local Times



Balayage of Additive Functionals



Processes with Identical Hitting Distributions



Dual Processes and Potential Theory



Dual Processes



Potentials of Measures



Potentials of Additive Functionals



Capacity and Related Topics


Notes and Comments


Bibliography


Index of Notation


Subject Index