6533b82efe1ef96bd1292742
RESEARCH PRODUCT
Approximation of exit times for one-dimensional linear diffusion processes
Samuel HerrmannNicolas Massinsubject
GeneralizationOrder (ring theory)Context (language use)Exit timeRandom walk010103 numerical & computational mathematicsStochastic algorithmRandom walk01 natural sciencesLinear diffusion010101 applied mathematicsComputational MathematicsComputational Theory and MathematicsDiffusion processPosition (vector)Modeling and SimulationApplied mathematicsGeneralized spheroids[MATH]Mathematics [math]0101 mathematicsDiffusion (business)Brownian motionMathematicsdescription
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 examples.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-09-15 | Computers & Mathematics with Applications |