First-Passage Time Distributions of a Brownian Motion Observed After a Random Delay
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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.
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View paper (DOI)Open access versionOpenAlexWSEAS TRANSACTIONS on SYSTEMS archivePublished 2026-09-29
Authors: Mario Lefebvre, Ibrahim Toure
Institutions: Polytechnique Montréal