Deaconu, Madalina; Herrmann, Samuel Simulation of hitting times for Bessel processes with non-integer dimension. (English) Zbl 1407.60110 Bernoulli 23, No. 4B, 3744-3771 (2017). Summary: 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 [Ann. Appl. Probab. 23, No. 6, 2259–2289 (2013; Zbl 1298.65018)], 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. Cited in 1 ReviewCited in 7 Documents MSC: 60J60 Diffusion processes 60G40 Stopping times; optimal stopping problems; gambling theory Keywords:Bessel processes with non-integer dimension; hitting time; numerical algorithm Citations:Zbl 1298.65018 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid