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On the first-exit time problem for temporally homogeneous Markov processes

Published online by Cambridge University Press:  14 July 2016

Henry C. Tuckwell
Henry C. Tuckwell*
Affiliation:
University of Chicagocor1corresp
*
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Abstract

Using an integral equation of Darling and Siegert in conjunction with the backward Kolmogorov equation for the transition probability density function, recurrence relations are derived for the moments of the time of first exit of a temporally homogeneous Markov process from a set in the phase space. The results, which are similar to those for diffusion processes, are used to find the expectation of the time between impulses of a Stein model neuron.

Keywords

FIRST-EXIT TIMESMARKOV PROCESSESRECURRENCE RELATIONSNEURON
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 39 - 48
Copyright
Copyright © Applied Probability Trust 1976 

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