On a first-passage problem for a cumulative process with exponential decay

Akira Tsurui and Shunji Osaki

Stochastic Processes and their Applications, 1976, vol. 4, issue 1, 79-88

Abstract: A first-passage problem for a cumulative process is investigated. The cumulative process is assumed to be generated by a Poisson process, and the amplitude generated by an event is assumed to decay exponentially. An integral equation for the probability density of the first-passage time until the total amplitude exceeds a pre-specified threshold level is derived. The Laplace transform of the probability density of the first-passage time is obtained explicity when each amplitude generated by an event is distributed exponentially. The mean first-passage times are given in a closed form and plotted versus the threshold level.

Keywords: secondary; process; Poisson; process; exponential; decay; threshold; first; passage (search for similar items in EconPapers)
Date: 1976
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Citations: View citations in EconPapers (4)

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