A filtered ASTA property
type: Item
instance of: scholarly article
title: A filtered ASTA property
zbMATH Open document ID: 0762.60090
DOI: 10.1007/BF01164002
author: Muhammad El-Taha
author: Shaler jun. Stidham
published in: Queueing Systems
publication date: 1993-01-17T00:00:00Z
review text: Recently, a considerable number of papers appeared where the PASTA (Poisson Arrivals See Time Averages) property, a notion coined by \textit{R. W. Wolff} [Oper. Res. 30, 223-231 (1982; Zbl 0489.60096)], has been extended to a more general framework. In particular, it has been shown that Poissonianity of a point process embedded in a continuous-time process is not necessary for the coincidence of embedded and non-embedded stationary distributions of the continuous-time process. The assumption that certain conditional intensities of the embedded point process are equal to its (unconditional) intensity turns out to be sufficient and necessary for the coincidence property mentioned. In the present paper, conditions are found which ensure that from the coincidence of embedded and non-embedded stationary distributions of the continuous-time process it follows that not only conditional and unconditional intensities are equal, but that, moreover, a certain conditional embedded point process as a whole is a probabilistic replica of the original (unconditional) one. Examples are given (e.g. Cox processes) for which these conditions are satisfied. A discrete-time version of these results has been obtained as well.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 98547
zbMATH Keywords: point processes
zbMATH Keywords: PASTA property
zbMATH Keywords: coincidence of embedded and non-embedded stationary distributions
zbMATH Keywords: sufficient and necessary for the coincidence property
reviewed by: Volker Schmidt
describes a project that uses: ASTA
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01164002
OpenAlex ID: W2008437796
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description: scientific article; zbMATH DE number 98547