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A discontinuous Galerkin method for approximating the stationary distribution of stochastic fluid-fluid processes

Citation

Bean, N and Lewis, A and Nguyen, GT and O'Reilly, MM and Sunkara, V, A discontinuous Galerkin method for approximating the stationary distribution of stochastic fluid-fluid processes, Methodology and Computing in Applied Probability pp. 1-42. ISSN 1387-5841 (2022) [Refereed Article]


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The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License, (https://creativecommons.org/licenses/by/4.0/) which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

DOI: doi:10.1007/s11009-022-09945-2

Abstract

The stochastic fluid-fluid model (SFFM) is a Markov process {(Xt, Yt, φt), t ≥ 0}, where {φt, t ≥ 0} is a continuous-time Markov chain, the first fluid, {Xt, t ≥ 0}, is a classical stochastic fluid process driven by {φt, t ≥ 0}, and the second fluid, {Yt, t ≥ 0}, is driven by the pair {(Xt, φt), t ≥ 0}. Operator-analytic expressions for the stationary distribution of the SFFM, in terms of the infinitesimal generator of the process {(Xt, φt), t ≥ 0}, are known. However, these operator-analytic expressions do not lend themselves to direct computation. In this paper the discontinuous Galerkin (DG) method is used to construct approximations to these operators, in the form of finite dimensional matrices, to enable computation. The DG approximations are used to construct approximations to the stationary distribution of the SFFM, and results are verified by simulation. The numerics demonstrate that the DG scheme can have a superior rate of convergence compared to other methods.

Item Details

Item Type:Refereed Article
Keywords:stochastic fluid-fluid processes, stationary distribution, discontinuous Galerkin method
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:150236
Year Published:2022
Deposited By:Mathematics
Deposited On:2022-06-03
Last Modified:2022-09-30
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