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

2019/06/07 by Herrmann, Samuel, Massin, Nicolas
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1906.02969

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 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.

Related

• Exit problem for Ornstein-Uhlenbeck processes: a random walk approach
• Exact simulation of first exit times for one-dimensional diffusion processes
• Exact simulation of diffusion first exit times: algorithm acceleration
• First time to exit of a continuous Itô process: general moment estimates and L1-convergence rate for discrete time approximations
• Strong approximation of particular one-dimensional diffusions