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Yaglom limit for stochastic fluid models
journal contribution
posted on 2023-05-21, 04:40 authored by Bean, NG, Malgorzata O'ReillyMalgorzata O'Reilly, Palmowski, ZIn 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.
Funding
Australian Research Council
History
Publication title
Advances in Applied ProbabilityVolume
53Pagination
649-686ISSN
0001-8678Department/School
School of Natural SciencesPublisher
Applied Probability TrustPlace of publication
The University, School Mathematics Statistics, Sheffield, England, S3 7RhRights statement
Copyright 2021 The Author(s)Repository Status
- Restricted