Bernoulli

  • Bernoulli
  • Volume 23, Number 4B (2017), 3744-3771.

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

Madalina Deaconu and Samuel Herrmann

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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.

Article information

Source
Bernoulli, Volume 23, Number 4B (2017), 3744-3771.

Dates
Received: December 2014
Revised: May 2016
First available in Project Euclid: 23 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1495505108

Digital Object Identifier
doi:10.3150/16-BEJ866

Mathematical Reviews number (MathSciNet)
MR3654822

Zentralblatt MATH identifier
06778302

Keywords
Bessel processes with non-integer dimension hitting time numerical algorithm

Citation

Deaconu, Madalina; Herrmann, Samuel. Simulation of hitting times for Bessel processes with non-integer dimension. Bernoulli 23 (2017), no. 4B, 3744--3771. doi:10.3150/16-BEJ866. https://projecteuclid.org/euclid.bj/1495505108


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