Derivative formulas and gradient estimates for SDEs driven by αα-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 αα-stable noises, where α∈(0,2)α∈(0,2). As an application, the strong Feller property for stochastic partial differential equations driven by subordinated cylindrical Brownian motions is presented.