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

^*此作品的通讯作者

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32 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	3195-3219
页数	25
期刊	Journal of Functional Analysis
卷	269
期	10
DOI	https://doi.org/10.1016/j.jfa.2015.09.007
出版状态	已出版 - 15 11月 2015
已对外发布	是

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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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AU - Xu, Lihu

AU - Zhang, Xicheng

PY - 2015/11/15

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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

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ER -

Gradient estimates for SDEs driven by multiplicative Lévy noise

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