Nash Inequalities for Markov Processes in Dimension One

摘要

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.