Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes

Jie Ming Wang

doi:10.1007/s10114-020-9459-1

Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes

Jie Ming Wang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation S^b= Δ ¯ ^α^/²+ b⋅ ∇ where Δ ¯ ^α^/² is the truncated fractional Laplacian, α ∈ (1, 2) and b ∈ K_d^α−1. In the second part, for a more general finite range jump process, we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance ∣x − y∣ in short time.

Original language	English
Pages (from-to)	229-248
Number of pages	20
Journal	Acta Mathematica Sinica, English Series
Volume	37
Issue number	2
DOIs	https://doi.org/10.1007/s10114-020-9459-1
Publication status	Published - Feb 2021

Keywords

47D07
47G20
60J35
60J75
Heat kernel
finite range jump process
gradient estimate
martingale problem
transition density function
truncated fractional Laplacian

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10.1007/s10114-020-9459-1

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title = "Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes",

abstract = "In this paper, we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation Sb= Δ ¯ α/2+ b⋅ ∇ where Δ ¯ α/2 is the truncated fractional Laplacian, α ∈ (1, 2) and b ∈ Kdα−1. In the second part, for a more general finite range jump process, we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance ∣x − y∣ in short time.",

keywords = "47D07, 47G20, 60J35, 60J75, Heat kernel, finite range jump process, gradient estimate, martingale problem, transition density function, truncated fractional Laplacian",

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T1 - Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes

AU - Wang, Jie Ming

PY - 2021/2

Y1 - 2021/2

N2 - In this paper, we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation Sb= Δ ¯ α/2+ b⋅ ∇ where Δ ¯ α/2 is the truncated fractional Laplacian, α ∈ (1, 2) and b ∈ Kdα−1. In the second part, for a more general finite range jump process, we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance ∣x − y∣ in short time.

AB - In this paper, we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation Sb= Δ ¯ α/2+ b⋅ ∇ where Δ ¯ α/2 is the truncated fractional Laplacian, α ∈ (1, 2) and b ∈ Kdα−1. In the second part, for a more general finite range jump process, we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance ∣x − y∣ in short time.

KW - 47D07

KW - 47G20

KW - 60J35

KW - 60J75

KW - Heat kernel

KW - finite range jump process

KW - gradient estimate

KW - martingale problem

KW - transition density function

KW - truncated fractional Laplacian

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DO - 10.1007/s10114-020-9459-1

M3 - Article

AN - SCOPUS:85097195914

SN - 1439-8516

VL - 37

SP - 229

EP - 248

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 2

ER -

Heat Kernel Estimates for Non-symmetric Finite Range Jump Processes

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