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January 2012 Sharp heat kernel estimates for relativistic stable processes in open sets
Zhen-Qing Chen, Panki Kim, Renming Song
Ann. Probab. 40(1): 213-244 (January 2012). DOI: 10.1214/10-AOP611


In this paper, we establish sharp two-sided estimates for the transition densities of relativistic stable processes [i.e., for the heat kernels of the operators m − (m2/α − Δ)α/2] in C1,1 open sets. Here m > 0 and α ∈ (0, 2). The estimates are uniform in m ∈ (0, M] for each fixed M > 0. Letting m ↓ 0, we recover the Dirichlet heat kernel estimates for Δα/2 := −(−Δ)α/2 in C1,1 open sets obtained in [14]. Sharp two-sided estimates are also obtained for Green functions of relativistic stable processes in bounded C1,1 open sets.


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Zhen-Qing Chen. Panki Kim. Renming Song. "Sharp heat kernel estimates for relativistic stable processes in open sets." Ann. Probab. 40 (1) 213 - 244, January 2012.


Published: January 2012
First available in Project Euclid: 3 January 2012

zbMATH: 1235.60101
MathSciNet: MR2917772
Digital Object Identifier: 10.1214/10-AOP611

Primary: 47G20 , 60J35 , 60J75
Secondary: 47D07

Keywords: Exit time , Green function , heat kernel , Lévy system , parabolic Harnack inequality , relativistic stable process , Symmetric α-stable process , Transition density

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 1 • January 2012
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