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Generalised reward generator for stochastic fluid models

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conference contribution
posted on 2023-05-23, 11:37 authored by Samuelson, A, Malgorzata O'ReillyMalgorzata O'Reilly, Bean, NB

We construct a generalised reward matrix Z(s). which is an extension of the fluid generator Q(s) of a stochastic fluid model (SFM). We classify the generators that are projections of Z(s), including the generator Q(s), and discuss the application of the resulting generators in different contexts.

As one application example, for the case with nonzero mean drift, we derive a new Riccati equation for the key matrix Ψ, which records the probabilities of the first return to the original level.

The Riccati equation has the form Ψ + ΨM-+Ψ = M+-, where parameters M+- and M-+ are block matrices in the matrix M, which records the expected number of visits to the original level, before the unbounded fluid drifts to ± ∞.

Finally, we derive the explicit form Ψ = M+- (I + M--)-1.

Funding

Australian Research Council

History

Publication title

Proceedings of the 9th International Conference on Matrix-Analytic Methods in Stochastic Models

Editors

QM He, G Horvath, M Telek

Pagination

27-34

ISBN

9781450321389

Department/School

School of Natural Sciences

Publisher

ACM

Place of publication

Budapest, Hungary

Event title

9th International Conference on Matrix-Analytic Methods in Stochastic Models

Event Venue

Budapest, Hungary

Date of Event (Start Date)

2016-06-28

Date of Event (End Date)

2016-06-30

Rights statement

Copyright unknown

Repository Status

  • Open

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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