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 α -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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