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Gauge theorems for resolvents with application to Markov processes
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  • Published: December 1991

Gauge theorems for resolvents with application to Markov processes

  • Karl-Theodor Sturm1 

Probability Theory and Related Fields volume 89, pages 387–406 (1991)Cite this article

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  • 7 Citations

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Summary

LetV=(V α)α≧0 be a (not necessarily sub-Markovian) resolvent such that the kernelV α for some α≧0 is compact and irreducible. We prove the following general gauge theorem: If there exists at least oneV-excessive function which is notV-inviriant, thenV 0 is bounded.

This result will be applied to resolventsU M arising from perturbation of sub-Markovian right resolventsU by multiplicative functionalsM (not necessarily supermartingale), for instance, by Feynman-Kac functionals. Among others, this leads to an extension of the gauge theorem of Chung/Rao and even of one direction of the conditional gauge theorem of Falkner and Zhao.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstrasse 1 1/2, W-8520, Erlangen, Federal Republic of Germany

    Karl-Theodor Sturm

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  1. Karl-Theodor Sturm
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Sturm, KT. Gauge theorems for resolvents with application to Markov processes. Probab. Th. Rel. Fields 89, 387–406 (1991). https://doi.org/10.1007/BF01199785

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  • Received: 10 April 1990

  • Revised: 01 March 1991

  • Issue Date: December 1991

  • DOI: https://doi.org/10.1007/BF01199785

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Keywords

  • Stochastic Process
  • Probability Theory
  • Markov Process
  • Mathematical Biology
  • General Gauge
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