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2006 Excursion theory revisited
P. J. Fitzsimmons, R. K. Getoor
Illinois J. Math. 50(1-4): 413-437 (2006). DOI: 10.1215/ijm/1258059481

Abstract

Excursions from a fixed point $b$ are studied in the framework of a general Borel right process $X$, with a fixed excessive measure $m$ serving as background measure; such a measure always exists if $b$ is accessible from every point of the state space of $X$. In this context the left-continuous moderate Markov dual process $\widehat X$ arises naturally and plays an important role. This allows the basic quantities of excursion theory such as the Laplace-L\'evy exponent of the inverse local time at $b$ and the Laplace transform of the entrance law for the excursion process to be expressed as inner products involving simple hitting probabilities and expectations. In particular if $X$ and $\widehat X$ are honest, then the resolvent of $X$ may be expressed entirely in terms of quantities that depend only on $X$ and $\widehat X$ killed when they first hit $b$.

Citation

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P. J. Fitzsimmons. R. K. Getoor. "Excursion theory revisited." Illinois J. Math. 50 (1-4) 413 - 437, 2006. https://doi.org/10.1215/ijm/1258059481

Information

Published: 2006
First available in Project Euclid: 12 November 2009

zbMATH: 1106.60062
MathSciNet: MR2247835
Digital Object Identifier: 10.1215/ijm/1258059481

Subjects:
Primary: 60J40
Secondary: 60G51, 60J45, 60J55

Rights: Copyright © 2006 University of Illinois at Urbana-Champaign

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Vol.50 • No. 1-4 • 2006
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