Derivative formulas and gradient estimates for SDEs driven by [formula omitted]-stable processes

Abstract

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.