Markov Processes and Potential Theory

, by Blumenthal, Robert M.; Getoor, Ronald K.

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ISBN: 9780486462639 | 0486462633
Cover: Paperback
Copyright: 12/17/2007

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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.

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Preface	p. iii
Preliminaries
Notation	p. 1
The Monotone Class Theorem	p. 5
Topological Spaces	p. 8
Markov Processes
General Definitions	p. 11
Transition Functions	p. 14
General Definitions Continued	p. 20
Equivalent Processes	p. 24
The Measures P[superscript mu]	p. 25
Stopping Times	p. 30
Stopping Times for Markov Processes	p. 36
The Strong Markov Property	p. 37
Standard Processes	p. 44
Measurability of Hitting Times	p. 52
Further Properties of Hitting Times	p. 61
Regular Step Processes	p. 63
Excessive Functions
Introduction	p. 69
Excessive Functions	p. 72
Exceptional Sets	p. 79
The Fine Topology	p. 84
Alternative Characterization of Excessive Functions	p. 89
Multiplicative Functionals and Subprocesses
Multiplicative Functionals	p. 97
Subordinate Semigroups	p. 101
Subprocesses	p. 105
Resolvents and Strong Multiplicative Functionals	p. 113
Excessive Functions	p. 125
A Theorem of Hunt	p. 136
Additive Functionals and Their Potentials
Additive Functionals	p. 148
Potentials of Additive Functionals	p. 154
Potentials of Continuous Additive Functionals	p. 160
Potentials of Natural Additive Functionals	p. 170
Classification of Excessive Functions	p. 186
Further Properties of Continuous Additive Functionals
Reference Measures	p. 196
Continuous Additive Functionals	p. 205
Fine Supports and Local Times	p. 212
Balayage of Additive Functionals	p. 228
Processes with Identical Hitting Distributions	p. 233
Dual Processes and Potential Theory
Dual Processes	p. 252
Potentials of Measures	p. 265
Potentials of Additive Functionals	p. 279
Capacity and Related Topics	p. 283
Notes and Comments	p. 295
Bibliography	p. 305
Index of Notation	p. 311
Subject Index	p. 312
Table of Contents provided by Ingram. All Rights Reserved.

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Markov Processes and Potential Theory

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