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 Type:	Refereed Article
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
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