Derivative formulae for SDEs driven by multiplicative α-stable-like processes

Linlin Wang; Longjie Xie; Xicheng Zhang

doi:10.1016/j.spa.2014.10.011

Derivative formulae for SDEs driven by multiplicative α-stable-like processes

Linlin Wang
, Longjie Xie^*
, Xicheng Zhang

^*此作品的通讯作者

School of Mathematics and Statistics
Wuhan University

科研成果: 期刊稿件 › 文章 › 同行评审

14 引用（Scopus）

摘要

By using Bismut's approach to the Malliavin calculus with jumps, we establish a derivative formula of Bismut-Elworthy-Li's type for SDEs driven by multiplicative Lévy noises, whose Lévy measure satisfies some order conditions. In particular, α-stable-like noises are allowed. Moreover, we also obtain the sharp gradient estimate in short time for the corresponding transition semigroup provided α∈(1,2).

源语言	英语
页（从-至）	867-885
页数	19
期刊	Stochastic Processes and their Applications
卷	125
期	3
DOI	https://doi.org/10.1016/j.spa.2014.10.011
出版状态	已出版 - 3月 2015
已对外发布	是

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abstract = "By using Bismut's approach to the Malliavin calculus with jumps, we establish a derivative formula of Bismut-Elworthy-Li's type for SDEs driven by multiplicative L{\'e}vy noises, whose L{\'e}vy measure satisfies some order conditions. In particular, α-stable-like noises are allowed. Moreover, we also obtain the sharp gradient estimate in short time for the corresponding transition semigroup provided α∈(1,2).",

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AU - Wang, Linlin

AU - Xie, Longjie

AU - Zhang, Xicheng

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N2 - By using Bismut's approach to the Malliavin calculus with jumps, we establish a derivative formula of Bismut-Elworthy-Li's type for SDEs driven by multiplicative Lévy noises, whose Lévy measure satisfies some order conditions. In particular, α-stable-like noises are allowed. Moreover, we also obtain the sharp gradient estimate in short time for the corresponding transition semigroup provided α∈(1,2).

AB - By using Bismut's approach to the Malliavin calculus with jumps, we establish a derivative formula of Bismut-Elworthy-Li's type for SDEs driven by multiplicative Lévy noises, whose Lévy measure satisfies some order conditions. In particular, α-stable-like noises are allowed. Moreover, we also obtain the sharp gradient estimate in short time for the corresponding transition semigroup provided α∈(1,2).

KW - Derivative formula

KW - Gradient estimate

KW - Malliavin calculus

KW - Stable-like process

UR - https://www.scopus.com/pages/publications/84919625595

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ER -

Derivative formulae for SDEs driven by multiplicative α-stable-like processes

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