Harnack Inequalities for SDEs Driven by Cylindrical α-Stable Processes

Linlin Wang; Xicheng Zhang

doi:10.1007/s11118-014-9451-4

Harnack Inequalities for SDEs Driven by Cylindrical α-Stable Processes

Linlin Wang, Xicheng Zhang^*

^*Corresponding author for this work

Wuhan University

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

21 Citations (Scopus)

Abstract

By using the coupling argument, we establish the Harnack and log-Harnack inequalites for stochastic differential equations with non-Lipschitz drifts and driven by additive anisotropic subordinated Brownian motions (in particular, cylindrical α-stable processes). Moreover, the gradient estimate is also derived when the drift is Lipschitz continuous.

Original language	English
Pages (from-to)	657-669
Number of pages	13
Journal	Potential Analysis
Volume	42
Issue number	3
DOIs	https://doi.org/10.1007/s11118-014-9451-4
Publication status	Published - 1 Apr 2015
Externally published	Yes

Keywords

Coupling method
Cylindrical α-stable process
Gradient estimate
Harnack inequality

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10.1007/s11118-014-9451-4

Cite this

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title = "Harnack Inequalities for SDEs Driven by Cylindrical α-Stable Processes",

abstract = "By using the coupling argument, we establish the Harnack and log-Harnack inequalites for stochastic differential equations with non-Lipschitz drifts and driven by additive anisotropic subordinated Brownian motions (in particular, cylindrical α-stable processes). Moreover, the gradient estimate is also derived when the drift is Lipschitz continuous.",

keywords = "Coupling method, Cylindrical α-stable process, Gradient estimate, Harnack inequality",

author = "Linlin Wang and Xicheng Zhang",

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AU - Wang, Linlin

AU - Zhang, Xicheng

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N2 - By using the coupling argument, we establish the Harnack and log-Harnack inequalites for stochastic differential equations with non-Lipschitz drifts and driven by additive anisotropic subordinated Brownian motions (in particular, cylindrical α-stable processes). Moreover, the gradient estimate is also derived when the drift is Lipschitz continuous.

AB - By using the coupling argument, we establish the Harnack and log-Harnack inequalites for stochastic differential equations with non-Lipschitz drifts and driven by additive anisotropic subordinated Brownian motions (in particular, cylindrical α-stable processes). Moreover, the gradient estimate is also derived when the drift is Lipschitz continuous.

KW - Coupling method

KW - Cylindrical α-stable process

KW - Gradient estimate

KW - Harnack inequality

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U2 - 10.1007/s11118-014-9451-4

DO - 10.1007/s11118-014-9451-4

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EP - 669

JO - Potential Analysis

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ER -

Harnack Inequalities for SDEs Driven by Cylindrical α-Stable Processes

Abstract

Keywords

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