On the convergence of Le Page series in Skohorod space

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.