The important and beautiful connection between Brownian motion and classical potential theory was first investigated by Kakutani [1], Kac [1],
and Doob [1]. Hunt [2] then showed that potential theory could be
developed by probabilistic methods for a large class of transient Markov
processes. There is now a large literature on potential theory for transient
Markov processes, including books by Dynkin [1], Ito and McKean [2],
Meyer [1], and Blumenthal and Getoor [1]. Recurrent potential theory
was first developed for random walks by Spitzer and for Markov chains
by Kemeny and Snell. Further work in this area has been done by a
number of people, including the present authors Port and Stone [1] and
Stone [1] (see books by Spitzer [1], Kemeny, Snell, and Knapp [1], and
Revuz [1]).