In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to systematically give gradient estimates for some important...

The paper is a continuation of our paper, Wang and Wang (2013) [13], Chen and Wang  [4], and it studies functional inequalities for non-local Dirichlet forms with finite range jumps or large jumps. Let α∈(0,2) and μV(dx)=CVe−V(x)dx be a probability measure. We present explicit and sharp...