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A Diffusion Model for a System Subject to Continuous Wear

Published online by Cambridge University Press:  27 July 2009

Laurence A. Baxter  and
Eui Yong Lee
Laurence A. Baxter
Affiliation:
Department of Applied Mathematics and StatisticsState University of New York at Stony Brook, Stony Brook, New York 11 794
Eui Yong Lee
Affiliation:
Department of Applied Mathematics and StatisticsState University of New York at Stony Brook, Stony Brook, New York 11 794
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Abstract

A model for a system whose state changes continuously with time is introduced. It is assumed that the system is modeled by Brownian motion with negative drift and an absorbing barrier at the origin. A repairman arrives according to a Poisson process and increases the state of the system by a random amount if the state is below a threshold α. Explicit expressions are deduced for the distribution function of X(t), the state of the system at time 1, if X(t) ≤ α and for the Laplace transform of the density of X( t). The stationary case is examined in detail.

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Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 4 , October 1987 , pp. 405 - 416
Copyright
Copyright © Cambridge University Press 1987

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References

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