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 journalArticle

17 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 languageEnglish
Pages (from-to)57-65
Number of pages9
JournalProbabilistic Engineering Mechanics
Volume20
Issue number1
DOIs
Publication statusPublished - Jan 2005
Externally publishedYes

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