Simulation of hitting times for Bessel processes with non integer dimension

Madalina Deaconu 1, 2 Samuel Herrmann 3
1 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
2 Probabilités et statistiques
IECL - Institut Élie Cartan de Lorraine
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 \cite{Deaconu-Herrmann}, 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.
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Article dans une revue
Bernoulli journal, 2016
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https://hal.archives-ouvertes.fr/hal-00933198
Contributeur : Samuel Herrmann <>
Soumis le : vendredi 13 mai 2016 - 16:29:26
Dernière modification le : mardi 20 septembre 2016 - 15:50:43
Document(s) archivé(s) le : mardi 16 août 2016 - 09:35:14

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Madalina Deaconu, Samuel Herrmann. Simulation of hitting times for Bessel processes with non integer dimension. Bernoulli journal, 2016. <hal-00933198v2>

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