Approximation of exit times for one-dimensional linear and growth diffusion processes

Samuel Herrmann (1) , Nicolas Massin (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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 in the Ornstein-Uhlenbeck context. 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 either a general linear diffusion or a growth diffusion. The efficiency of the method is described with particular care through theoretical results and numerical examples.

Mots clés: growth diffusion; linear diffusion; exit time; stochastic algorithm; generalized spheroids; random walk

Domaines: Probabilités [math.PR]

Samuel Herrmann, Nicolas Massin. Approximation of exit times for one-dimensional linear and growth diffusion processes. 2019. ⟨hal-02147874v2⟩