On the convergence of Le Page series in Skohorod space

Youri Davydov (1) , Clément Dombry (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 6086]

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.

Keywords: stable distribution; Le Page series; Skohorod space

Domains: Probability [math.PR]

Youri Davydov, Clément Dombry. On the convergence of Le Page series in Skohorod space. 2011. ⟨hal-00607964⟩