We prove Cheng-Yau type inequalities for positive harmonic functions on Riemannian manifolds by using methods of Stochastic Analysis. Rather than evaluating an exact Bismut formula for the differential of a harmonic function, our method relies on a Bismut type inequality which is derived by an...

We consider the operatorWe prove existence and uniqueness of solutions to the martingale problem for this operator under appropriate conditions on the aij,bi, and [lambda]i. The process corresponding to solves an infinite dimensional stochastic differential equation similar to that for the...

We give a new proof of the well-known fact that the pinned Wiener measure on a Lie group is quasi-invariant under right multiplication by finite energy paths. The main technique we use is the time reversal. This approach is different from what B. Driver used to prove quasi-invariance for the...