Approximation of exit times for one-dimensional linear diffusion processes. (15th September 2020)

• Record Type: Journal Article
• Authors: Herrmann, Samuel; Massin, Nicolas
• Is Part Of: Computers & mathematics with applications. Volume 80:issue 6(2020)
• Page Start: 1668
• Page End: 1682
• Publication Date: 2020-09-15
• Subjects: Exit time -- Linear diffusion -- Random walk -- Generalized spheroids -- Stochastic algorithm; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2020.07.023
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: 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.