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First-passage and first-exit times of a Bessel-like stochastic process

Martin, E; Behn, U; Germano, G; (2011) First-passage and first-exit times of a Bessel-like stochastic process. Physical Review E , 83 (5) 10.1103/PhysRevE.83.051115. Green open access

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Abstract

We study a stochastic process X t which is a particular case of the Rayleigh process and whose square is the Bessel process, with various applications in physics, chemistry, biology, economics, finance, and other fields. The stochastic differential equation is dX t = ( nD / X t ) dt + √ 2 D dW t , where W t is the Wiener process. The drift term can arise from a logarithmic potential or from taking X t as the norm of a multidimensional random walk. Due to the singularity of the drift term for X t = 0 , different natures of boundary at the origin arise depending on the real parameter n : entrance, exit, and regular. For each of them we calculate analytically and numerically the probability density functions of first-passage times or first-exit times. Nontrivial behavior is observed in the case of a regular boundary.

Type: Article
Title: First-passage and first-exit times of a Bessel-like stochastic process
Open access status: An open access version is available from UCL Discovery
DOI: 10.1103/PhysRevE.83.051115
Publisher version: https://doi.org/10.1103/PhysRevE.83.051115
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10125099
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