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arXiv · 2204.01419

Stability of estimates for fundamental solutions under Feynman-Kac perturbations for symmetric Markov processes

Daehong Kim·Panki Kim·Kazuhiro Kuwae
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Abstract

In this paper, when a given symmetric Markov process X satisfies the stability of global heat kernel two-sided (upper) estimates by Markov perturbations, we give a necessary and sufficient condition on the stability of global two-sided (upper) estimates for fundamental solution of Feynman-Kac semigroup of X. As a corollary, under the same assumptions, a weak type global two-sided (upper) estimates holds for the fundamental solution of Feynman-Kac semigroup with (extended) Kato class conditions for measures. This generalizes all known results on the stability of global integral kernel estimates by symmetric Feynman-Kac perturbations with Kato class conditions in the framework of symmetric Markov processes.

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Daehong Kim, Panki Kim, Kazuhiro Kuwae. 2022-04-04. Stability of estimates for fundamental solutions under Feynman-Kac perturbations for symmetric Markov processes. https://arxiv.org/abs/2204.01419

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