Exact simulation of the first-passage time of diffusions

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.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01524814
Contributeur : Samuel Herrmann <>
Soumis le : jeudi 18 mai 2017 - 18:29:59
Dernière modification le : lundi 22 mai 2017 - 16:43:34
Document(s) archivé(s) le : lundi 21 août 2017 - 00:24:30

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FPT-Torino-2017-05.pdf
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  • HAL Id : hal-01524814, version 1
  • ARXIV : 1705.06881

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Samuel Herrmann, Cristina Zucca. Exact simulation of the first-passage time of diffusions. 2017. 〈hal-01524814〉

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