Stability of estimates for fundamental solutions under Feynman-Kac perturbations for symmetric Markov processes
Probability
2022-04-05 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.2204.01419,
title = {Stability of estimates for fundamental solutions under Feynman-Kac perturbations for symmetric Markov processes},
author = {Daehong Kim and Panki Kim and Kazuhiro Kuwae},
journal= {arXiv preprint arXiv:2204.01419},
year = {2022}
}