In this paper. we give characterizations of Nash inequalities for birth-death process anddiffusion process on the line. As a by-product. we prove that for these processes. transience impliesthat 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 Markoviancoupling with respect to a non-negative lower semi-continuous function is proved.As an application ofthis result,the well-known Strassen’s theorem is generalized.Moreover,it is proved that the existence ofan order-preserving Markovian coupling of two given jump processes is equivalent to their stochasticalcomparability.
Shaoyi ZhangDepartment of Mathematics.Beijing Normal University,Beijing 100875,P.R.China Department of Mathematics,Hubei Normal University,Huangshi 435002,P.R.China
