https://u-bourgogne.hal.science/hal-02570881Herrmann, 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 first exit times for one-dimensional diffusion processesHAL CCSD2020Exit timeBrownian motiondiffusion processesGirsanov's transformationrejection samplingexact simulationrandomized algorithmconditioned Brownian motion[MATH.MATH-PR] Mathematics [math]/Probability [math.PR][MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]université de Bourgogne, IMB -2020-05-12 14:28:252023-03-24 14:53:162020-05-12 14:28:25enJournal articles10.1051/m2an/20190771The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability horizontal ellipsis The usual procedure is to use discretization schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study are the Girsanov transformation, the convergent series method for the simulation of random variables and the classical rejection sampling. The efficiency of the method is described through theoretical results and numerical examples.