Almost Sure Continuity of Stable Moving Average Processes with Index Less Than One

Abstract

Rootzen (1978) gives a sufficient condition for sample continuity of moving average processes with respect to stable motion with index $\alpha$ less than two. We provide a simple proof of this criterion for $\alpha < 1$ and show that the condition is then also necessary for continuity of the process. The same result holds for the moving-maximum process. A description of the local behaviour of the sample functions of such processes is given.