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Yaglom limit for stochastic fluid models
Citation
Bean, NG and O'Reilly, MM and Palmowski, Z, Yaglom limit for stochastic fluid models, Advances in Applied Probability, 53, (3) pp. 649-686. ISSN 0001-8678 (2021) [Refereed Article]
Copyright Statement
Copyright 2021 The Author(s)
Abstract
In this paper we provide the analysis of 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, transient and stationary analyses of the SFMs have been only 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 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, Ψ(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.
Item Details
Item Type: | Refereed Article |
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Keywords: | yaglom limit, stochastic fluid models, Markov chains, Laplace-Stieltjes transform, limiting conditional distribution |
Research Division: | Mathematical Sciences |
Research Group: | Statistics |
Research Field: | Stochastic analysis and modelling |
Objective Division: | Expanding Knowledge |
Objective Group: | Expanding knowledge |
Objective Field: | Expanding knowledge in the mathematical sciences |
UTAS Author: | O'Reilly, MM (Associate Professor Malgorzata O'Reilly) |
ID Code: | 148161 |
Year Published: | 2021 |
Funding Support: | Australian Research Council (LP140100152) |
Deposited By: | Mathematics |
Deposited On: | 2021-12-07 |
Last Modified: | 2022-05-04 |
Downloads: | 0 |
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