Gradient estimates for SDEs driven by multiplicative Lévy noise

By Feng-Yu Wang, Lihu Xu, Xicheng Zhang. 2013

57 citations recorded by the source corpus.

Abstract Gradient estimates are derived, for the first time, for the semigroup associated to a class of stochastic differential equations driven by multiplicative Levy 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.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9aba76e6e20690db0f608791191d6d8c07d51e29