On the convergence of Le Page series in Skohorod space

TL;DR

This paper investigates the convergence conditions of Le Page series in Skohorod space, offering a simple criterion based on moments to determine the existence of stable distributions with specified spectral measures.

Contribution

It introduces a straightforward criterion for the convergence of Le Page series in Skohorod space based on moments of the process increments.

Findings

Provided a simple sufficient condition for convergence.

Established criteria for the existence of stable distributions.

Linked moments of process increments to convergence in Skohorod space.

Abstract

We consider the problem of the convergence of the so-called Le Page series in the Skohorod space $\bbD^d=\bbD([0,1],\bbR^d)$ and provide a simple criterion based on the moments of the increments of the random process involved in the series. This provides a simple sufficient condition for the existence of an $\alpha$-stable distribution on $\bbD^d$ with given spectral measure.