Electronic Communications in Probability

Further studies on square-root boundaries for Bessel processes

Larbi Alili and Hiroyuki Matsumoto

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Abstract

We look at decompositions of perpetuities and apply them to the study of the distributions of hitting times of Bessel processes of two types of square root boundaries. These distributions are linked giving a new proof of some Mellin transforms results obtained by DeLong [6] and Yor [17]. Several random factorizations and characterizations of the studied distributions are established.

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 39, 9 pp.

Dates
Received: 21 May 2018
Accepted: 29 May 2018
First available in Project Euclid: 20 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1529460064

Digital Object Identifier
doi:10.1214/18-ECP139

Mathematical Reviews number (MathSciNet)
MR3820129

Zentralblatt MATH identifier
1397.60079

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60J65: Brownian motion [See also 58J65]
Secondary: 60G18: Self-similar processes 60J60: Diffusion processes [See also 58J65]

Keywords
Bessel processes exponential functionals random affine equations square-root boundaries

Rights
Creative Commons Attribution 4.0 International License.

Citation

Alili, Larbi; Matsumoto, Hiroyuki. Further studies on square-root boundaries for Bessel processes. Electron. Commun. Probab. 23 (2018), paper no. 39, 9 pp. doi:10.1214/18-ECP139. https://projecteuclid.org/euclid.ecp/1529460064


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References

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