Electronic Communications in Probability

On the supremum of products of symmetric stable processes

Christophe Profeta

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

lower tail probability persistence probability stable processes

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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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