Approximate factorizations for non-symmetric jump processes

2025/04/20 by Cho, Soobin, Song, Renming · 1 citation
#35K08 #47G20 #60J45 #60J50 #60J76 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2504.14763

Abstract

In this paper, we first extend the approximate factorization for purely discontinuous Markov process established in \citeCKSV20 by getting rid of some of the conditions imposed in \citeCKSV20. 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 \citeKW24 in C^{1, ε} 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∈ (0, 2) and of censored α-stable processes in C^1, \rm Dini open sets for all α∈ (1, 2).

Cited by

• Abnormal boundary decay for stable operators

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