Derivative formulae for SDEs driven by multiplicative α-stable-like processes
Linlin Wang,
Longjie Xie and
Xicheng Zhang
Stochastic Processes and their Applications, 2015, vol. 125, issue 3, 867-885
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).
Keywords: Derivative formula; Gradient estimate; Stable-like process; Malliavin calculus (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:3:p:867-885
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DOI: 10.1016/j.spa.2014.10.011
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