Characterization of almost surely continuous 1-stable random Fourier series and strongly stationary processes (Q919703)

This paper completes the work of \textit{M. B. Marcus} and \textit{G. Pisier}, Acta Math. 152, 245-301 (1984; Zbl 0547.60047), concerning sample path continuity for strongly stationary p-stable processes on a locally compact Abelian group, in the case \(p=1\). Their necessary condition (finiteness of a certain entropy integral) is shown to be sufficient. The method used here also provides an alternative approach to the sufficient conditions of Marcus and Pisier for \(p>1\).