Hitting time for correlated three-dimensional Brownian motion

Let X = (X1;X2;X3) be a three-dimensional correlated Brownian motion and T i be the first hitting time of a fixed level by Xi. The purpose of this paper is to compute the joint density of T = inf(T1, T2, T3) and X_T . We prove that the method of images used in dimension two by Iyengar leads us to a tiling three-dimensional space problem. A such a problem has only some particular solutions.

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Source https://hal.science/hal-00846450
Author Blanchet-Scalliet, Christophette, Cousin, Areski, Dorobantu, Diana
Maintainer CCSD
Last Updated May 9, 2026, 07:05 (UTC)
Created May 9, 2026, 07:05 (UTC)
Identifier hal-00846450
Language en
Rights https://about.hal.science/hal-authorisation-v1/
contributor Institut Camille Jordan (ICJ) ; École Centrale de Lyon (ECL) ; Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL) ; Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon) ; Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM) ; Université Jean Monnet (EPSCPE) (UJM EPE)-Université Jean Monnet (EPSCPE) (UJM EPE)-Centre National de la Recherche Scientifique (CNRS)
creator Blanchet-Scalliet, Christophette
date 2013-07-19T00:00:00
harvest_object_id e6eb45a0-e636-4856-87f8-d26cbc35a935
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2026-04-23T00:00:00
set_spec type:UNDEFINED