Exact simulation of the first-passage time of diffusionsReport as inadecuate




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1 IMB - Institut de Mathématiques de Bourgogne Dijon 2 University of Torino

Abstract : Since diffusion processes arise in so many different fields, efficient tech-nics 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.

Keywords : Brownian motion 2010 AMS subject classifications: primary 65C05 randomized algorithm exact simulation Girsanov-s transformation cesses diffusion pro- 60G40 secondary: 65N75 and phrases: first-passage time





Author: Samuel Herrmann - Cristina Zucca -

Source: https://hal.archives-ouvertes.fr/



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