Approximate factorizations for non-symmetric jump processes

Fuente: arXiv
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Autori principali: Cho, Soobin, Song, Renming
Natura: Preprint
Pubblicazione: 2025
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author Cho, Soobin
Song, Renming
author_facet Cho, Soobin
Song, Renming
contents In this paper, we first extend the approximate factorization for purely discontinuous Markov process established in \cite{CKSV20} by getting rid of some of the conditions imposed in \cite{CKSV20}. Then we apply the approximate factorization to obtain sharp two-sided heat kernel estimates for three classes of processes: stable-like processes with critical killings in $C^{1, {\rm Dini}}$ open sets; killed stable-like processes in the setting of \cite{KW24} in $C^{1, \varepsilon}$ open sets; and non-symmetric stable processes in what we call $C^{1,2{\text - \rm Dini}}$ open sets. In particular, we obtain explicit sharp two-sided heat kernel estimates of killed $α$-stable processes in $C^{1, {\rm Dini}}$ open sets for all $α\in (0, 2)$ and of censored $α$-stable processes in $C^{1, {\rm Dini}}$ open sets for all $α\in (1, 2)$.
format Preprint
id arxiv_https___arxiv_org_abs_2504_14763
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Approximate factorizations for non-symmetric jump processes
Cho, Soobin
Song, Renming
Probability
Analysis of PDEs
60J45, 60J50, 60J76, 47G20, 35K08
In this paper, we first extend the approximate factorization for purely discontinuous Markov process established in \cite{CKSV20} by getting rid of some of the conditions imposed in \cite{CKSV20}. Then we apply the approximate factorization to obtain sharp two-sided heat kernel estimates for three classes of processes: stable-like processes with critical killings in $C^{1, {\rm Dini}}$ open sets; killed stable-like processes in the setting of \cite{KW24} in $C^{1, \varepsilon}$ open sets; and non-symmetric stable processes in what we call $C^{1,2{\text - \rm Dini}}$ open sets. In particular, we obtain explicit sharp two-sided heat kernel estimates of killed $α$-stable processes in $C^{1, {\rm Dini}}$ open sets for all $α\in (0, 2)$ and of censored $α$-stable processes in $C^{1, {\rm Dini}}$ open sets for all $α\in (1, 2)$.
title Approximate factorizations for non-symmetric jump processes
topic Probability
Analysis of PDEs
60J45, 60J50, 60J76, 47G20, 35K08
url https://arxiv.org/abs/2504.14763