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A note on the infinitely deep dam with a Markovian input

Published online by Cambridge University Press:  14 July 2016

R. M. Phatarfod
R. M. Phatarfod*
Affiliation:
Monash University
*
∗Postal address: Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.
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Abstract

In this paper we consider an infinitely deep dam fed by inputs which form an ergodic Markov chain and whose release M is non-unit. The extension to non-unit release follows on lines similar to the independent inputs case. We show that P(θ) – θ MΙ where P(θ) = (pijθ i) has a maximum of N = M(M + l)/2 non-zero singularities in the unit disc, so that the general solution of the equilibrium equations has N unknown constants. We also show that these constants satisfy N linear constraints, so that the solution is fully determined.

Keywords

INFINITELY DEEP DAMNON-UNIT RELEASEMARKOV INPUT
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 4 , December 1979 , pp. 917 - 922
Copyright
Copyright © Applied Probability Trust 1979 

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