Heat Kernels for Non-symmetric Non-local Operators

Zhen Qing Chen; Xicheng Zhang

doi:10.1515/9783110571561-003

Heat Kernels for Non-symmetric Non-local Operators

Zhen Qing Chen, Xicheng Zhang

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

12 Citations (Scopus)

Abstract

We survey some recent progress in the study of heat kernels for a class of non-symmetric non-local operators. We focus on the existence and sharp two-sided estimates of the heat kernels and their connection to jump diffusions.

Original language	English
Title of host publication	Recent developments in Nonlocal Theory
Publisher	de Gruyter
Pages	24-51
Number of pages	28
ISBN (Electronic)	9783110571561
ISBN (Print)	9783110571554
DOIs	https://doi.org/10.1515/9783110571561-003
Publication status	Published - 1 Jan 2018
Externally published	Yes

Keywords

Discontinuous Markov process
Lévy system
diffusion with jumps
heat kernel estimate
non-local operator
pseudo-differential operator

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10.1515/9783110571561-003

Cite this

Chen, Z. Q., & Zhang, X. (2018). Heat Kernels for Non-symmetric Non-local Operators. In Recent developments in Nonlocal Theory (pp. 24-51). de Gruyter. https://doi.org/10.1515/9783110571561-003

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keywords = "Discontinuous Markov process, L{\'e}vy system, diffusion with jumps, heat kernel estimate, non-local operator, pseudo-differential operator",

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AB - We survey some recent progress in the study of heat kernels for a class of non-symmetric non-local operators. We focus on the existence and sharp two-sided estimates of the heat kernels and their connection to jump diffusions.

KW - Discontinuous Markov process

KW - Lévy system

KW - diffusion with jumps

KW - heat kernel estimate

KW - non-local operator

KW - pseudo-differential operator

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BT - Recent developments in Nonlocal Theory

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Heat Kernels for Non-symmetric Non-local Operators

Abstract

Keywords

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