Recurrence Type Characterisation of mu-Exponential Ergodicity for MarkovProcesses

摘要

The paper studies a characterization of mu-exponential ergodicity through thetotal expected mu-rewards until absorption into a finite set, for regular, standard, conservative Markov processes on a countable state space. This total expected reward condition is closely related to Tweedie's necessary and sufficient condition for exponential ergodicity, which uses the intensity matrix. Our condition can also be interpreted as a condition on the mu-norm of the taboo transition probability matrix. If the Markov process is uniformizable, the properties of our interest can be studied through an approximating discrete time Markov chain. The applicability of the total mu-reward condition is illustrated by its verification for the Jackson network with an arbitrary, but finite number of servers in each node.