论文标题
在Feynman-KAC扰动下对对称Markov过程的基本解决方案的估计稳定性
Stability of estimates for fundamental solutions under Feynman-Kac perturbations for symmetric Markov processes
论文作者
论文摘要
在本文中，当给定的对称马尔可夫过程x满足了通过马尔可夫扰动来满足全球热内核双面估计的稳定性时，我们给出了全球两侧（上）的稳定性的必要和足够条件，用于X.属于全球的基本估计（在同一型号的情况下）（属于全球型号）的基本解决方案，该解决方案（一个差异）（一个差异）（一个差异）（一个差异）（一个差异）（一个差异）（一个型号）（一个型号）（一个型号）。 Feynman-kac Semigroup具有（延长的）Kato类条件的措施。这概括了所有已知的结果，这些结果涉及对称对称的马尔可夫工艺框架中对称的Feynman-kac扰动的全球积分内核估计的稳定性。
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.
