Mario Lefebvre, Ibrahim Touré, "First-Passage Time Distributions of a Brownian Motion Observed After a Random Delay," WSEAS Transactions on Systems, vol. 25, pp. 654-658, 2026, DOI:10.37394/23202.2026.25.52
Mario Lefebvre, Ibrahim Touré. First-Passage Time Distributions of a Brownian Motion Observed After a Random Delay.
WSEAS Transactions on Systems. 2026;25:654-658. 10.37394/23202.2026.25.52
WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 25, 2026
First-Passage Time Distributions of a Brownian Motion Observed After a Random Delay
Authors: ,
Abstract: Suppose that a Brownian motion can only be observed after a random time τ . We are interested in
the distribution of the time T required to record the first visit to a given threshold. The cases when τ has an
exponential and an Erlang distribution are considered. A method to approximate the probability density function
of T from its moments is also presented.
Keywords:
Wiener process, Erlang distribution, convolution, moments, orthogonal polynomials, Laguerre
polynomials
Pages: 654-658 WSEAS Transactions on Systems, ISSN / E-ISSN: 1109-2777 / 2224-2678, Volume 25, 2026, Art. #52 DOI: 10.37394/23202.2026.25.52
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