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https://hdl.handle.net/2440/133674
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Type: | Journal article |
Title: | Yaglom limit for stochastic fluid models |
Author: | Bean, N.G. O'Reilly, M.M. Palmowski, Z. |
Citation: | Advances in Applied Probability, 2021; 53(3):649-686 |
Publisher: | Cambridge University Press |
Issue Date: | 2021 |
ISSN: | 0001-8678 1475-6064 |
Statement of Responsibility: | NIGEL G. BEAN, MAŁGORZATA M. O, REILLY, ZBIGNIEW PALMOWSKI |
Abstract: | In this paper we analyse the limiting conditional distribution (Yaglom limit) for stochastic fluid models (SFMs), a key class of models in the theory of matrix-analytic methods. So far, only transient and stationary analyses of SFMs have been considered in the literature. The limiting conditional distribution gives useful insights into what happens when the process has been evolving for a long time, given that its busy period has not ended yet. We derive expressions for the Yaglom limit in terms of the singularity˜s∗ such that the key matrix of the SFM, (s), is finite (exists) for all s ≥ s∗ and infinite for s < s∗. We show the uniqueness of the Yaglom limit and illustrate the application of the theory with simple examples. |
Keywords: | Stochastic fluid model; Markov chain; Laplace–Stieltjes transform; Yaglom limit; limiting conditional distribution |
Rights: | © The Author(s) 2021. Published by Cambridge University Press on behalf of Applied Probability Trust |
DOI: | 10.1017/apr.2020.71 |
Grant ID: | http://purl.org/au-research/grants/arc/LP140100152 |
Published version: | http://dx.doi.org/10.1017/apr.2020.71 |
Appears in Collections: | Mathematical Sciences publications |
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