Electronic Communications in Probability

On the supremum of products of symmetric stable processes

Christophe Profeta

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Abstract

We study the asymptotics, for small and large values, of the supremum of a product of symmetric stable processes. We show in particular that the lower tail exponent remains the same as for only one process, possibly up to some logarithmic terms. The proof relies on a path construction of stable bridges using last sign changes.

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 97, 13 pp.

Dates
Received: 11 May 2018
Accepted: 13 November 2018
First available in Project Euclid: 18 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1545102493

Digital Object Identifier
doi:10.1214/18-ECP193

Mathematical Reviews number (MathSciNet)
MR3896835

Zentralblatt MATH identifier
07023483

Subjects
Primary: 60G52: Stable processes 60J65: Brownian motion [See also 58J65]

Keywords
lower tail probability persistence probability stable processes

Rights
Creative Commons Attribution 4.0 International License.

Citation

Profeta, Christophe. On the supremum of products of symmetric stable processes. Electron. Commun. Probab. 23 (2018), paper no. 97, 13 pp. doi:10.1214/18-ECP193. https://projecteuclid.org/euclid.ecp/1545102493


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