Transient Boundary Theory

Abstract

For purposes of motivation it is convenient to think of the state space of a Markov chain P with only transient states as being similar to the open unit disk of two-dimensional Euclidean space. In two-space the boundary of the disk—namely the circle S¹—has the property that there is a one-one correspondence between the non-negative harmonic functions $h(r{e^{i\theta }})$ in the disk and the non-negative Borel measures µ^h on the circle.