https://hal-univ-bourgogne.archives-ouvertes.fr/hal-02173732Herrmann, SamuelSamuelHerrmannIMB - Institut de Mathématiques de Bourgogne [Dijon] - UB - Université de Bourgogne - UBFC - Université Bourgogne Franche-Comté [COMUE] - CNRS - Centre National de la Recherche ScientifiqueZucca, CristinaCristinaZuccaDipartimento di Matematica "Giuseppe Peano" [Torino] - UNITO - Università degli studi di Torino = University of TurinExact Simulation of the First-Passage Time of DiffusionsHAL CCSD2019First-passage timeBrownian motionDiffusion processesGirsanov's transformationExact simulationRandomized algorithm[MATH] Mathematics [math]université de Bourgogne, IMB -2019-07-04 16:24:262022-12-11 09:11:372019-07-04 16:24:26enJournal articles10.1007/s10915-018-00900-31Since diffusion processes arise in so many different fields, efficient technics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations of the first-passage times as a by-product. For efficiency reasons, it is particularly challenging to simulate directly this hitting time by avoiding to construct the whole paths. In the Brownian case, the distribution of the first-passage time is explicitly known and can be easily used for simulation purposes. The authors introduce a new rejection sampling algorithm which permits to perform an exact simulation of the first-passage time for general one-dimensional diffusion processes. The efficiency of the method, which is essentially based on Girsanov's transformation, is described through theoretical results and numerical examples.