HARNACK INEQUALITY FOR SDE WITH MULTIPLICATIVENOISE AND EXTENSION TO NEUMANN SEMIGROUP ONNONCONVEX MANIFOLDS1

摘要

By constructing a coupling with unbounded time-dependent drift, dimension-free Harnack inequalities are established for a large class of sto-chastic differential equations with multiplicative noise. These inequalities are applied to the study of heat kernel upper bound and contractivity properties of the semigroup. The main results are also extended to reflecting diffusion processes on Riemannian manifolds with nonconvex boundary.