Exact simulation of the first-passage time of diffusions
Herrmann, Samuel ; Zucca, Cristina
HAL, hal-01524814 / Harvested from HAL
Text on HAL
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.
Publié le : 2017-05-18
Classification:  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,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-01524814,
     author = {Herrmann, Samuel and Zucca, Cristina},
     title = {Exact simulation of the first-passage time of diffusions},
     journal = {HAL},
     volume = {2017},
     number = {0},
     year = {2017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01524814}
}

Herrmann, Samuel; Zucca, Cristina. Exact simulation of the first-passage time of diffusions. HAL, Tome 2017 (2017) no. 0, . http://gdmltest.u-ga.fr/item/hal-01524814/