Since 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.

Exact Simulation of the First-Passage Time of Diffusions

Zucca, C.
2019

Abstract

Since 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.
79
3
1477
1504
https://arxiv.org/abs/1705.06881
First-passage time, Brownian motion, Diffusion processes, Girsanov’s transformation, Exact simulation, Randomized algorithm
Herrmann, S.; Zucca, C.
File in questo prodotto:
File Dimensione Formato  
Herrmann-Zucca2019_Article_ExactSimulationOfTheFirst-Pass.pdf

Accesso riservato

Tipo di file: PDF EDITORIALE
Dimensione 999.32 kB
Formato Adobe PDF
999.32 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2318/1686120
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 6
social impact