Simulation of hitting times for Bessel processes with non integer dimension

TL;DR

This paper develops a new algorithm for simulating hitting times of Bessel processes with non-integer dimensions, extending previous methods that only applied to integer dimensions, with applications in finance and neuroscience.

Contribution

The paper introduces a novel simulation algorithm for non-integer dimension Bessel processes using the additivity property of squared Bessel laws, expanding prior integer-based methods.

Findings

New algorithm effectively simulates hitting times for non-integer dimensions.

Method leverages additivity property of squared Bessel processes.

Applicable to fields like finance and neuroscience.

Abstract

In this paper we pursue and complete the study of the simulation of the hitting time of some given boundaries for Bessel processes. These problems are of great interest in many application fields as finance and neurosciences. In a previous work, the authors introduced a new method for the simulation of hitting times for Bessel processes with integer dimension. The method was based mainly on the explicit formula for the distribution of the hitting time and on the connexion between the Bessel process and the Euclidean norm of the Brownian motion. This method does not apply anymore for a non integer dimension. In this paper we consider the simulation of the hitting time of Bessel processes with non integer dimension and provide a new algorithm by using the additivity property of the laws of squared Bessel processes. We split each simulation step in two parts: one is using the integer dimension case and the other one considers hitting time of a Bessel process starting from zero.