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2018 Estimates of Dirichlet heat kernels for subordinate Brownian motions
Panki Kim, Ante Mimica
Electron. J. Probab. 23: 1-45 (2018). DOI: 10.1214/18-EJP190

Abstract

In this paper, we discuss estimates of transition densities of subordinate Brownian motions in open subsets of Euclidean space. When $D$ is a $C^{1,1}$ domain, we establish sharp two-sided estimates for the transition densities of a large class of subordinate Brownian motions in $D$ whose scaling order is not necessarily strictly below $2$. Our estimates are explicit and written in terms of the dimension, the Euclidean distance between two points, the distance to the boundary and the Laplace exponent of the corresponding subordinator only.

Citation

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Panki Kim. Ante Mimica. "Estimates of Dirichlet heat kernels for subordinate Brownian motions." Electron. J. Probab. 23 1 - 45, 2018. https://doi.org/10.1214/18-EJP190

Information

Received: 2 September 2017; Accepted: 13 June 2018; Published: 2018
First available in Project Euclid: 26 July 2018

zbMATH: 06924676
MathSciNet: MR3835470
Digital Object Identifier: 10.1214/18-EJP190

Subjects:
Primary: 60J35, 60J50, 60J75
Secondary: 47G20

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