On the supremum of products of symmetric stable processes

TL;DR

This paper investigates the extreme values of the product of symmetric stable processes, revealing that the persistence exponent remains unchanged from a single process, aside from logarithmic factors.

Contribution

It provides new asymptotic results for the supremum of products of symmetric stable processes, highlighting the persistence exponent's invariance.

Findings

Persistence exponent is unchanged for the product, compared to a single process.

Asymptotic behavior of the supremum is characterized for small and large values.

Logarithmic terms appear in the asymptotic analysis.

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 persistence exponent remains the same as for only one process, up to some logarithmic terms.