STABLE MIXED MOVING AVERAGES

The class of (non-Gaussian) stable moving average processes is extende d by introducing an appropriate joint randomization of the filter func tion and of the stable noise, leading to stable mixed moving averages. Their distribution determines a certain combination of the filter fun ction and the mixing measure, leading to a generalization of a theorem of Kanter (1973) for usual moving averages. Stable mixed moving avera ges contain sums of independent stable moving averages, are ergodic an d are not harmonizable. Also a class of stable mixed moving averages i s constructed with the reflection positivity property.