Gradient estimates for SDEs driven by multiplicative Lévy noise

Feng Yu Wang; Lihu Xu; Xicheng Zhang

doi:10.1016/j.jfa.2015.09.007

Gradient estimates for SDEs driven by multiplicative Lévy noise

Feng Yu Wang^*, Lihu Xu, Xicheng Zhang

^*Corresponding author for this work

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

33 Citations (Scopus)

Abstract

Gradient estimates are derived, for the first time, for the semigroup associated to a class of stochastic differential equations driven by multiplicative Lévy noise. In particular, the estimates are sharp for α-stable type noises. To derive these estimates, a new derivative formula of Bismut-Elworthy-Li's type is established for the semigroup by using the Malliavin calculus and a finite-jump approximation argument.

Original language	English
Pages (from-to)	3195-3219
Number of pages	25
Journal	Journal of Functional Analysis
Volume	269
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2015.09.007
Publication status	Published - 15 Nov 2015
Externally published	Yes

Keywords

Derivative formula
Gradient estimate
Lévy process
Time-change

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10.1016/j.jfa.2015.09.007

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title = "Gradient estimates for SDEs driven by multiplicative L{\'e}vy noise",

abstract = "Gradient estimates are derived, for the first time, for the semigroup associated to a class of stochastic differential equations driven by multiplicative L{\'e}vy noise. In particular, the estimates are sharp for α-stable type noises. To derive these estimates, a new derivative formula of Bismut-Elworthy-Li's type is established for the semigroup by using the Malliavin calculus and a finite-jump approximation argument.",

keywords = "Derivative formula, Gradient estimate, L{\'e}vy process, Time-change",

author = "Wang, {Feng Yu} and Lihu Xu and Xicheng Zhang",

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year = "2015",

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doi = "10.1016/j.jfa.2015.09.007",

language = "English",

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T1 - Gradient estimates for SDEs driven by multiplicative Lévy noise

AU - Wang, Feng Yu

AU - Xu, Lihu

AU - Zhang, Xicheng

PY - 2015/11/15

Y1 - 2015/11/15

N2 - Gradient estimates are derived, for the first time, for the semigroup associated to a class of stochastic differential equations driven by multiplicative Lévy noise. In particular, the estimates are sharp for α-stable type noises. To derive these estimates, a new derivative formula of Bismut-Elworthy-Li's type is established for the semigroup by using the Malliavin calculus and a finite-jump approximation argument.

AB - Gradient estimates are derived, for the first time, for the semigroup associated to a class of stochastic differential equations driven by multiplicative Lévy noise. In particular, the estimates are sharp for α-stable type noises. To derive these estimates, a new derivative formula of Bismut-Elworthy-Li's type is established for the semigroup by using the Malliavin calculus and a finite-jump approximation argument.

KW - Derivative formula

KW - Gradient estimate

KW - Lévy process

KW - Time-change

UR - http://www.scopus.com/inward/record.url?scp=84943451197&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2015.09.007

DO - 10.1016/j.jfa.2015.09.007

M3 - Article

AN - SCOPUS:84943451197

SN - 0022-1236

VL - 269

SP - 3195

EP - 3219

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 10

ER -

Gradient estimates for SDEs driven by multiplicative Lévy noise

Abstract

Keywords

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