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arXiv · 1301.4528

Gradient estimates for SDEs Driven by Multiplicative L\'evy Noise

Feng-Yu Wang·Lihu Xu·Xicheng Zhang
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Abstract

Gradient estimates are derived, for the first time, for the semigroup associated to a class of stochastic differential equations driven by multiplicative L\'evy noise. In particular, the estimates are sharp for $\alpha$-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.

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Feng-Yu Wang, Lihu Xu, Xicheng Zhang. 2013-01-19. Gradient estimates for SDEs Driven by Multiplicative L\'evy Noise. https://arxiv.org/abs/1301.4528

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