Blumenthal R.M., Getoor R.K. Markov processes and potential theory

NY/London: Academic press, 1968. - 314p.Preliminaries.
Notation.
The Monotone Class Theorem.
Topological Spaces.
Chapter I. Markov processes.
General Definitions.
Transition Functions.
General Definitions Continued.
Equivalent Processes.
The Measures P^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.
Chapter II. Excessive functions.Excessive Functions.
Exceptional Sets.
The Fine Topology.
Alternative Characterization of Excessive Functions.
Chapter III. Multiplicative functionals and subprocesses.
Multiplicative Functional.
Subordinate Semigroups.
Subprocesses.
Resolvents and Strong Multiplicative Functional.
Excessive Functions.
A Theorem of Hunt.
Chapter IV. 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.
Chapter V. 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.
Chapter VI. Dual processes and potential theory.
Dual Processes.
Potentials of Measures.
Potentials of Additive Functionals.
Capacity and Related Topics.
Notes and Comments.Index of Notation.
Subject Index.
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