Simulation of hitting times for Bessel processes with non-integer dimension

Madalina Deaconu 1, 2, * Samuel Herrmann 3
* Corresponding author
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : In this paper, we complete and improve the study of the simulation of the hitting times 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 (Ann. Appl. Probab. 23 (2013) 2259–2289), the authors introduced a new method for the simulation of hitting times for Bessel processes with integer dimension. The method, called walk on moving spheres algorithm (WoMS), was based mainly on the explicit formula for the distribution of the hitting time and on the connection 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 $\delta\geq1$ and provide a new algorithm by using the additivity property of the laws of squared Bessel processes. We split each simulation step of the algorithm in two parts: one is using the integer dimension case and the other one considers hitting time of a Bessel process starting from zero.
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Madalina Deaconu, Samuel Herrmann. Simulation of hitting times for Bessel processes with non-integer dimension. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2017, 23 (4B), pp.3744 - 3771. ⟨10.3150/16-BEJ866⟩. ⟨hal-00933198v2⟩

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