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

Yasushi Masuda

doi:10.1016/0304-4149(88)90027-0

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

Yasushi Masuda

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	51-63
Number of pages	13
Journal	Stochastic Processes and their Applications
Volume	29
Issue number	1
DOIs	https://doi.org/10.1016/0304-4149(88)90027-0
Publication status	Published - 1988
Externally published	Yes

Keywords

birth death processes
complete monotonicity
generalized phase type distributions
simple random walks
uniformization

ASJC Scopus subject areas

Statistics and Probability
Modelling and Simulation
Applied Mathematics

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10.1016/0304-4149(88)90027-0

Cite this

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AB - 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 birth-death process and simple random walks is also analyzed.

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KW - complete monotonicity

KW - generalized phase type distributions

KW - simple random walks

KW - uniformization

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

Abstract

Keywords

ASJC Scopus subject areas

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