Bulletin of the Belgian Mathematical Society - Simon Stevin

On the remarkable Lamperti representation of the inverse local time of a radial Ornstein-Uhlenbeck process

Francis Hirsch and Marc Yor

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Abstract

We give a description, in terms of ``pseudo-stable increasing process'', of the Lamperti process associated with the inverse local time of a radial Ornstein-Uhlenbeck process. Following Bertoin-Yor, we also express, in two particular cases, the law of the perpetuity associated with this inverse local time.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 20, Number 3 (2013), 435-449.

Dates
First available in Project Euclid: 4 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1378314508

Mathematical Reviews number (MathSciNet)
MR3129051

Zentralblatt MATH identifier
1287.60048

Subjects
Primary: 60J55: Local time and additive functionals 60J60: Diffusion processes [See also 58J65]
Secondary: 60E07: Infinitely divisible distributions; stable distributions 60G18: Self-similar processes 60G52: Stable processes

Keywords
local time Lamperti's correspondence Lamperti process Ornstein-Uhlenbeck process Bessel process perpetuity

Citation

Hirsch, Francis; Yor, Marc. On the remarkable Lamperti representation of the inverse local time of a radial Ornstein-Uhlenbeck process. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 3, 435--449. https://projecteuclid.org/euclid.bbms/1378314508


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