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 geometric quantities
under the Ricci flow, the mean curvature flow, the forced mean curvature flow
and the Yamabe flow respectively. Our conclusion gives another example that
probabilistic tools can be used to simplify proofs for some problems in
geometric analysis.Comment: 22 pages. Minor revision to v1. Accepted for publication in
Stochastic Processes and their Application
