First passage times of birth-death processes and simple random walks (Q1105921)

Although attached to a graduate school of management, this author reports on some research in essentially pure mathematics. 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 discrepancy between the first passage time structures of a birth-death process and simple random walks is also analyzed.