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The expected first-passage time for a sufficient statistic arising in the Poisson disorder problem

Published online by Cambridge University Press:  14 July 2016

K. Wickwire
K. Wickwire*
Affiliation:
University of Birmingham
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Abstract

In the Poisson disorder problem the probability that the parameter of a Poisson process y, has increased by a constant amount, given observations of ys, s ≦ t, is a Markov process of mixed type with jumps of variable (state-dependent) magnitude superimposed upon a drift which satisfies an ordinary differential equation. Using a likelihood-ratio transformation, one can reduce the backward equation satisfied by the expected first-passage time to a constant level for the mixed process to a differential-difference equation with a constant retardation. We discuss a method for solving this equation and present some numerical results on its solution. The accuracy of some approximations which are easier to calculate is investigated.

Keywords

POISSON DISORDER PROBLEMEXPECTED FIRST-PASSAGE TIMESMIXED PROCESSESDIFFERENTIAL-DIFFERENCE EQUATIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 274 - 286
Copyright
Copyright © Applied Probability Trust 1979 

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References

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