On some properties of Poisson processes
type: Item
instance of: scholarly article
title: On some properties of Poisson processes
zbMATH Open document ID: 0651.60088
DOI: 10.1007/BF01666518
author: Xisuo Liu
author: Guanghui Xu
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 1985-01-01T00:00:00Z
review text: The Poisson process, i.e., the simple stream, is defined by \textit{A. Ya. Khintchine} [Mathematical methods in the theory of queueing (1955; Zbl 0068.120)] as a stationary, orderly and finite stream without aftereffects. A necessary and sufficient condition for a stream to be a simple stream is that the interarrival times are independent random variables with identical exponential distributions. This paper gives a simple and rigorous proof of the necessary and sufficient condition, and discusses the other necessary and sufficient conditions for a renewal process to be a Poisson process.
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 4062311
zbMATH Keywords: Poisson process
zbMATH Keywords: necessary and sufficient conditions for a renewal process to be a Poisson process
MaRDI profile type: Publication
cites work: Q4197800
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full work available at URL: https://doi.org/10.1007/bf01666518
OpenAlex ID: W1977382721
description: scientific article; zbMATH DE number 4062311