Gradient estimates for SDEs driven by multiplicative L茅vy noise

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• 作者：Feng-Yu Wang^a ; ^b ; ^{wangfy@bnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{F.Y.Wang@swansea.ac.uk" class="auth_mail" title="E-mail the corresponding author} ; Lihu Xu^c ; Xicheng Zhang^d ; ^e
• 关键词：60H15 ; 35R60
• 刊名：Journal of Functional Analysis
• 出版年：2015
• 出版时间：15 November 2015
• 年：2015
• 卷：269
• 期：10
• 页码：3195-3219
• 全文大小：420 K

文摘

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 伪-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.