First Passage Time of Filtered Poisson Process with Exponential Shape Function

Alexander Novikov; Robert Melchers; Eka Shinjikashvili; Nino Kordzakhia

Abstract

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Solving some integro-differential equation we find the Laplace transformation 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 accuracy is veryfying with the help of Monte-Carlo simulations.

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