Markov Processes: Ray Processes and Right Processes

Getoor, R. K.

doi:10.1007/bfb0070061

Cited by 163 publications

(62 citation statements)

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“…NOTATION. Most of the notation we use is standard and can be found in [1] and [2], with one glaring exception which we shall discuss later. We shall use the symbol = to mean "is defined to be".…”

Section: Introductionmentioning

confidence: 99%

Riesz decompositions in Markov process theory

Getoor¹,

Glover²

1984

Trans. Amer. Math. Soc.

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Section: Introductionmentioning

confidence: 99%

Riesz decompositions in Markov process theory

Getoor¹,

Glover²

1984

Trans. Amer. Math. Soc.

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“…Under ( SF) one may use the original topology in defining the co-Ray compactification E as remarked at the end of the first paragraph of Section 5. But then (15.1) and (15.3) of [12] imply that the co-Ray topology agrees with the original topology. Therefore those results are corollaries of the results in this section.…”

Section: Discussionmentioning

confidence: 80%

“…See [19, §17-18] or [12]. Since this is a Ray-Knight compactification of E , is regarded as an ordinary trap in the definition of E. Thus U q ( , ·) = ε and U q (x, ({ })) = q −1 P x [e −qζ ] for x ∈ E, q > 0.…”

Section: Preliminariesmentioning

confidence: 99%

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Potential Theory of Moderate Markov Dual Processes

Fitzsimmons

Getoor

2009

Potential Anal

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Let X be a Borel right Markov process, let m be an excessive measure for X, and let X be the moderate Markov dual process associated with X and m. The potential theory of co-excessive measures (i.e., measures that are excessive for X) is developed with special emphasis on the Riesz decomposition. This is then applied to obtain the Riesz decomposition of excessive functions (of X) by exploiting the correspondence between such functions and co-excessive measures. The potential theory of co-excessive measures also enables us to discuss Walsh's interior réduite under minimal conditions. Many of the tools of the theory of Markov processes are employed in this development. For example, Kuznetsov measures, Ray compactifications, h-transforms, and duality theory for Borel right processes.

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“…We shall use the standard notation ( [1], [5]) of Markov processes without special mention. The following notation and minimal hypothesis will remain in force throughout.…”

Section: Section 0 Notationmentioning

confidence: 99%

A Riesz decomposition theorem

Graversen

1989

Nagoya Mathematical Journal

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The topic of this note is the Riesz decomposition of excessive functions for a “nice” strong Markov process X. I.e. an excessive function is decomposed into a sum of a potential of a measure and a “harmonic” function. Originally such decompositions were studied by G.A. Hunt [8]. In [1] a Riesz decomposition is given assuming that the state space E is locally compact with a countable base and X is a transient standard process in strong duality with another standard process having a strong Feller resolvent. Recently R.K. Getoor and J. Glover extended the theory to the case of transient Borei right processes in weak duality [6].

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Markov Processes: Ray Processes and Right Processes

Cited by 163 publications

References 0 publications

Riesz decompositions in Markov process theory

Riesz decompositions in Markov process theory

Potential Theory of Moderate Markov Dual Processes

A Riesz decomposition theorem

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