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Gradient estimates for SDEs Driven by Multiplicative Lévy Noise (1301.4528v2)
Published 19 Jan 2013 in math.PR and math.AP
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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