On a first-passage problem for a cumulative process with exponential decay |
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Authors: | Akira Tsurui Shunji Osaki |
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Affiliation: | Faculty of Engineering, Hiroshima University, Hiroshima 730, Japan |
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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. |
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Keywords: | secondary process Poisson process exponential decay threshold first passage |
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