Potential Theory for ergodic Markov chains (with a discrete state spare and a continuous parameter) is developed in terms of the fundamental matrix of a chain. A notion of an ergodic potential for a chain is introduced and a form of Riesz decomposition theorem for measures is proved. Ergodic...

A Markov chain (with a discrete state space and a continuous parameter) is perturbed by forcing a chain to return to "permissible" states whenever it happens to enter "forbidden" states, with returns governed by a replacement distribution. The compensation method is employed to obtain the...