Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10527365 | Stochastic Processes and their Applications | 2014 | 29 Pages |
Abstract
In this paper, we study sharp Dirichlet heat kernel estimates for a large class of symmetric Markov processes in C1,η open sets. The processes are symmetric pure jump Markov processes with jumping intensity κ(x,y)Ï1(|xây|)â1|xây|âdâα, where αâ(0,2). Here, Ï1 is an increasing function on [0,â), with Ï1(r)=1 on 01 for βâ[0,â], and κ(x,y) is a symmetric function confined between two positive constants, with |κ(x,y)âκ(x,x)|â¤c5|xây|Ï for |xây|<1 and Ï>α/2. We establish two-sided estimates for the transition densities of such processes in C1,η open sets when ηâ(α/2,1]. In particular, our result includes (relativistic) symmetric stable processes and finite-range stable processes in C1,η open sets when ηâ(α/2,1].
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Kyung-Youn Kim, Panki Kim,