0000000000724947
AUTHOR
Nicolas Massin
showing 2 related works from this author
First hitting time for a diffusion
2021
In this thesis, we focus our attention on the generation of the first exit time or the first passage time for diffusions in a one-dimensional context.In the first chapter, we present already well-known methods in order to generate such random variables. We particularly introduce the WOMS algorithm. This algorithm permits the generation of an approximation of the time needed by the Brownian motion in order to exit from a given interval.In the second and third chapters, we explain how to extend the previous algorithm in order to deal with diffusions strongly linked to the one-dimensional Brownian motion. We first consider the Ornstein-Uhlenbeck process, and then we consider a wide class of di…
Approximation of exit times for one-dimensional linear diffusion processes
2020
International audience; In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and the Ornstein-Uhlenbeck context, that is for particular time-homogeneous diffusion processes. Here the aim is therefore to generalize this efficient numerical approach in order to obtain an approximation of both the exit time and position for a general linear diffusion. The main challenge of such a generalization is to handle with time-inhomogeneous diffusions. The efficiency of the method is described with particular care through theoretical results and numerical example…