In this paper. we give characterizations of Nash inequalities for birth-death process and diffusion process on the line. As a by-product. we prove that for these processes. transience implies that the semigroups P(t) decay as ‖P(t)‖_(1--x)≤Ct^(-1). Sufficient conditions for general Msrkov chains are also obtained.
MAO Yong Hua Department of Mathematics. Beijing Normal University. Beijing 100875. P. R. China
In this paper,for two given transition probabilities,the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is proved.As an application of this result,the well-known Strassen’s theorem is generalized.Moreover,it is proved that the existence of an order-preserving Markovian coupling of two given jump processes is equivalent to their stochastical comparability.
Shaoyi ZhangDepartment of Mathematics.Beijing Normal University,Beijing 100875,P.R.China Department of Mathematics,Hubei Normal University,Huangshi 435002,P.R.China
