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

^*Corresponding author for this work

Wuhan University

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

14 Citations (Scopus)

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 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).

Original language	English
Pages (from-to)	867-885
Number of pages	19
Journal	Stochastic Processes and their Applications
Volume	125
Issue number	3
DOIs	https://doi.org/10.1016/j.spa.2014.10.011
Publication status	Published - Mar 2015
Externally published	Yes

Keywords

Derivative formula
Gradient estimate
Malliavin calculus
Stable-like process

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10.1016/j.spa.2014.10.011

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title = "Derivative formulae for SDEs driven by multiplicative α-stable-like processes",

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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author = "Linlin Wang and Longjie Xie and Xicheng Zhang",

year = "2015",

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T1 - Derivative formulae for SDEs driven by multiplicative α-stable-like processes

AU - Wang, Linlin

AU - Xie, Longjie

AU - Zhang, Xicheng

PY - 2015/3

Y1 - 2015/3

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

U2 - 10.1016/j.spa.2014.10.011

DO - 10.1016/j.spa.2014.10.011

M3 - Article

AN - SCOPUS:84919625595

SN - 0304-4149

VL - 125

SP - 867

EP - 885

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 3

ER -

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

Abstract

Keywords

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