Derivative formulas and gradient estimates for SDEs driven by -stable processes

In this paper we prove a derivative formula of Bismut–Elworthy–Li’s type as well as a gradient estimate for stochastic differential equations driven by α -stable noises, where α ∈ ( 0 , 2 ) . As an application, the strong Feller property for stochastic partial differential equations driven by subordinated cylindrical Brownian motions is presented.