This paper shows that row-continuous Markov chains with one or two boundaries have transient probabilities with matrix-geometric structure. Also explored is the relationship between the Green's function method and the matrix-geometric structure. Also explored is the relationship between the...

It is known that the first passage time of a birth death process from n to n+1 has a completely monotone density, however, the discrete analogue for a simple random walk does not hold. In this paper, first passage times of simple random walks from n to n+1 and from 0 to n are characterized. This...