First passage time of filtered Poisson process with exponential shape function

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Journal Article
Probabilistic Engineering Mechanics, 2005, 20 (1), pp. 57 - 65
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Solving some integro-differential equation we find the Laplace transform of the first passage time for filtered Poisson process generated by pulses with uniform or exponential distributions. Also, the martingale technique is applied for approximations of expectations and distributions of the first passage times. The approximations accuracy is verified with the help of Monte-Carlo simulations. © 2004 Elsevier Ltd. All rights reserved.
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