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

被引：1

作者：

Kim, Daehong ^{[1
]}

Kim, Panki ^{[2
,3
]}

Kuwae, Kazuhiro ^{[4
]}

机构：

[1] Technol Kumamoto Univ, Fac Adv Sci, Kumamoto 8608555, Japan

[2] Seoul Natl Univ, Dept Math Sci, Bldg 27,1 Gwanak Ro, Seoul 08826, South Korea

[3] Seoul Natl Univ, Res Inst Math, Bldg 27,1 Gwanak Ro, Seoul 08826, South Korea

[4] Fukuoka Univ, Dept Appl Math, Fukuoka 8140180, Japan

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2023年 / 75卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

Feynman-Kac perturbation; symmetric Markov processes; Dirichlet forms; heat kernel; spectral function; continuous additive functional of zero energy; Kato class; Green-tight measures; conditionally Green-tight measures; HEAT KERNELS; DIRICHLET FORMS; STOCHASTIC CALCULUS; HARNACK INEQUALITY; GAUGEABILITY; SUBCRITICALITY; FUNCTIONALS; OPERATORS; BOUNDS;

D O I：

10.2969/jmsj/88038803

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, when a given symmetric Markov process X satisfies the stability of global heat kernel two-sided (upper) estimates by Markov perturbations (see Definition 1.2), 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 of 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.

引用

页码：527 / 572

页数：46

共 50 条

[31] ANALYTIC CHARACTERIZATIONS OF GAUGEABILITY FOR GENERALIZED FEYNMAN-KAC FUNCTIONALS [J].

Kim, Daehong ;

Kuwae, Kazuhiro .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 369 (07) :4545-4596

[32] LARGE DEVIATION PRINCIPLES FOR GENERALIZED FEYNMAN-KAC FUNCTIONALS AND ITS APPLICATIONS [J].

Kim, Daehong ;

Kuwae, Kazuhiro ;

Tawara, Yoshihiro .

TOHOKU MATHEMATICAL JOURNAL, 2016, 68 (02) :161-197

[33]

Kuwae K, 1998, OSAKA J MATH, V35, P683

[34]

Kuwae K., 2006, Adv. Stud. Pure Math., V44, P193

[35] STOCHASTIC CALCULUS OVER SYMMETRIC MARKOV PROCESSES WITHOUT TIME REVERSAL [J].

Kuwae, Kazuhiro .

ANNALS OF PROBABILITY, 2010, 38 (04) :1532-1569

[36]

LEJAN Y, 1978, B SOC MATH FR, V106, P61

[37]

Ma Z.-M., 1992, Introduction to the Theory of (Non-Symmetric) Dirichlet Forms

[38] Lp-Kato class measures and their relations with Sobolev embedding theorems for Dirichlet spaces [J].

Mori, Takahiro .

JOURNAL OF FUNCTIONAL ANALYSIS, 2021, 281 (03)

[39] COMPOSITE MEDIA AND ASYMPTOTIC DIRICHLET FORMS [J].

MOSCO, U .

JOURNAL OF FUNCTIONAL ANALYSIS, 1994, 123 (02) :368-421

[40] Two-sided estimates on the density of the Feynman-Kac semigroups of stable-like processes [J].

Song, RM .

ELECTRONIC JOURNAL OF PROBABILITY, 2006, 11 :146-161

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