First passage time of filtered Poisson process with exponential shape function

Title: First passage time of filtered Poisson process with exponential shape function
Creator: Novikov, A.; Melchers, Robert E.; Shinjikashvili, E.; Kordzakhia, N.
Relation: Probabilistic Engineering Mechanics Vol. 20, no. 1, p. 57-65
Publisher: Computational Mechanics Publications
Resource Type: journal article
Date: 2005
Description: 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.
Subject: first passage times; laplace transform; martingales; integro-differential equations; filtered Poisson process; Omstein-Uhlenbeck process; gaussian random-walks
Identifier: uon:425
Identifier: http://hdl.handle.net/1959.13/25302
Identifier: ISSN:0266-8920
Language: eng
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