Markov Processes and Potential TheoryThis advanced text explores the relationship between Markov processes and potential theory, in addition to aspects of the theory of additive functionals. Geared toward graduate students, Markov Processes and Potential Theory assumes a familiarity with general measure theory, while offering a nearly self-contained treatment. 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. Exercises appear throughout the text, and a selection of notes and comments features historical references and credits. Robert M. Blumenthal is Professor Emeritus of Mathematics at the University of Washington, and Ronald K. Getoor is Professor Emeritus of Mathematics at the University of California at San Diego. |
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Markov Processes and Potential Theory Robert McCallum Blumenthal,Ronald Kay Getoor Snippet view - 1968 |
Markov Processes and Potential Theory Robert McCallum Blumenthal,Ronald Kay Getoor Snippet view - 2007 |
Common terms and phrases
a-excessive A₁ additive functionals assume B₁ Borel measurable Borel set Borel subset bounded Brownian motion Chapter Clearly compact subset complete the proof condition Consequently COROLLARY countable D₁ decreasing define definition denote equivalent excessive function exists F₁ fine topology finite measure fixed follows G₁ given hence Hint hypothesis implies increasing sequence inf{t left-hand limits Lemma Let f Let ƒ Let G M₁ Markov process Markov property measurable space natural potential nearly Borel measurable nonnegative notation o-algebra obtain open sets polar set probability measure proof of Theorem PROPOSITION prove quasi-left-continuous reader regular result right continuous MF satisfies semigroup semipolar set sequence of stopping standard process suffices to show supermartingale Supp(A Suppose surely T₁ T₂ topology transition function u₁ uª(x uniformly integrable vanishes X₁ zero