Gauge theorems for resolvents with application to Markov processes |
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Authors: | Karl-Theodor Sturm |
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Institution: | (1) Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstrasse 1 1/2, W-8520 Erlangen, Federal Republic of Germany |
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Abstract: | Summary LetV=(V
)0 be a (not necessarily sub-Markovian) resolvent such that the kernelV
for some 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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Keywords: | |
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