$Φ$-Entropy Inequality and Invariant Probability Measure for SDEs with Jump

Feng-Yu Wang

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arXiv · 1309.0942

$Φ$-Entropy Inequality and Invariant Probability Measure for SDEs with Jump

Feng-Yu Wang

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Abstract

By using the $Φ$-entropy inequality derived in \cite{Wu, Ch} for Poisson measures, the same type of inequality is established for a class of stochastic differential equations driven by purely jump Lévy processes. The semigroup $Φ$-entropy inequality for SDEs driven by Poisson point processes as well as a sharp result on the existence of invariant probability measures are also presented.

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Feng-Yu Wang. 2013-09-05. $Φ$-Entropy Inequality and Invariant Probability Measure for SDEs with Jump. https://arxiv.org/abs/1309.0942

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