On first passage time structure of random walks
type: Item
instance of: scholarly article
title: On first passage time structure of random walks
zbMATH Open document ID: 0574.60071
DOI: 10.1016/0304-4149(85)90021-3
author: Ushio Sumita
author: Yasushi Masuda
published in: Stochastic Processes and their Applications
publication date: 1985-01-01T00:00:00Z
review text: For continuous time birth-death processes on \({\mathbb{N}}\) the first passage time \(\tau_{n,n+1}\) from n to \(n+1\) is always a mixture of \(n+1\) exponential random variables. Furthermore the first passage time \(\tau_{0,n}\) is the sum of n independent exponential random variables. For a discrete time birth-death process the results are similar, replacing the exponential distributions by appropriate geometric ones. However if one allows the process to stay with certain probabilities in the same state, the above may not be true. The authors give necessary and sufficient conditions on the transition probabilities such that \(\tau_{n,n+1}\), \(\tau_{0,n}\) is a mixture, sum of geometric random variables.
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60E10
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 3917392
zbMATH Keywords: first passage times
zbMATH Keywords: conditional first passage times
zbMATH Keywords: strong unimodality
zbMATH Keywords: birth-death processes
zbMATH Keywords: exponential random variables
Wikidata QID: Q57549497
reviewed by: Uwe Rösler
MaRDI profile type: Publication
full work available at URL: 0304-4149(85)90021-3
OpenAlex ID: W1976383288
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description: scientific article; zbMATH DE number 3917392