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

AbstractIt 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 birth-death process and simple random walks is also analyzed