Gradient estimates for SDEs Driven by Multiplicative Lévy Noise

Abstract

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 $\alpha$-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.

21pp

References in corpus (6)

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Cited by in corpus (4)

• Degenerate SDE with Hölder-Dini Drift and Non-Lipschitz Noise Coefficient
• Stochastic flows for Lévy processes with Hölder drifts
• Integration by Parts Formula and Applications for SDEs with Lévy Noise
• Uniform Hölder Estimates on Semigroups Generated by Non-Local Operators of Variable Order