supported by National Natural Science Foundation of China(Grant No.11101433);the Fundamental Research Funds for the Central South University(Grant No.2011QNZT105);Doctorial Dissertation Program of Hunan Province(Grant No.YB2011B009);US National Science Foundation (Grant Nos.AMC-SS-0706713,DMS-0805929,NSFC-6398100 and CAS-2008DP173182)
Consider a family of probability measures {vξ} on a bounded open region D C Rd with a smooth boundary and a positive parameter set {βξ}, all indexed by ξ∈δD. For any starting point inside D, we run a diffusion u...