First passage time of filtered Poisson process with exponential shape function

A. Novikov; R. E. Melchers; E. Shinjikashvili; N. Kordzakhia

doi:10.1016/j.probengmech.2004.04.005

First passage time of filtered Poisson process with exponential shape function

A. Novikov^*, R. E. Melchers, E. Shinjikashvili, N. Kordzakhia

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	57-65
Number of pages	9
Journal	Probabilistic Engineering Mechanics
Volume	20
Issue number	1
DOIs	https://doi.org/10.1016/j.probengmech.2004.04.005
Publication status	Published - Jan 2005
Externally published	Yes

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10.1016/j.probengmech.2004.04.005

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title = "First passage time of filtered Poisson process with exponential shape function",

abstract = "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.",

author = "A. Novikov and Melchers, \{R. E.\} and E. Shinjikashvili and N. Kordzakhia",

year = "2005",

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T1 - First passage time of filtered Poisson process with exponential shape function

AU - Novikov, A.

AU - Melchers, R. E.

AU - Shinjikashvili, E.

AU - Kordzakhia, N.

PY - 2005/1

Y1 - 2005/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/10844230917

U2 - 10.1016/j.probengmech.2004.04.005

DO - 10.1016/j.probengmech.2004.04.005

M3 - Article

AN - SCOPUS:10844230917

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VL - 20

SP - 57

EP - 65

JO - Probabilistic Engineering Mechanics

JF - Probabilistic Engineering Mechanics

IS - 1

ER -

First passage time of filtered Poisson process with exponential shape function

Abstract

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