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September 2019 Heat kernel estimates for symmetric jump processes with mixed polynomial growths
Joohak Bae, Jaehoon Kang, Panki Kim, Jaehun Lee
Ann. Probab. 47(5): 2830-2868 (September 2019). DOI: 10.1214/18-AOP1323

Abstract

In this paper, we study the transition densities of pure-jump symmetric Markov processes in $\mathbb{R}^{d}$, whose jumping kernels are comparable to radially symmetric functions with mixed polynomial growths. Under some mild assumptions on their scale functions, we establish sharp two-sided estimates of the transition densities (heat kernel estimates) for such processes. This is the first study on global heat kernel estimates of jump processes (including non-Lévy processes) whose weak scaling index is not necessarily strictly less than 2. As an application, we proved that the finite second moment condition on such symmetric Markov process is equivalent to the Khintchine-type law of iterated logarithm at infinity.

Citation

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Joohak Bae. Jaehoon Kang. Panki Kim. Jaehun Lee. "Heat kernel estimates for symmetric jump processes with mixed polynomial growths." Ann. Probab. 47 (5) 2830 - 2868, September 2019. https://doi.org/10.1214/18-AOP1323

Information

Received: 1 May 2018; Revised: 1 November 2018; Published: September 2019
First available in Project Euclid: 22 October 2019

zbMATH: 07145304
MathSciNet: MR4021238
Digital Object Identifier: 10.1214/18-AOP1323

Subjects:
Primary: 60J35, 60J75
Secondary: 60F99

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 5 • September 2019
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