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

Samuel Herrmann; Nicolas Massin

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arXiv · 1906.02969

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

Samuel Herrmann·Nicolas Massin

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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.

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Samuel Herrmann, Nicolas Massin. 2019-06-07. Approximation of exit times for one-dimensional linear and growth diffusion processes. https://arxiv.org/abs/1906.02969

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