Summary
The class of (non-Gaussian) stable moving average processes is extended by introducing an appropriate joint randomization of the filter function and of the stable noise, leading to stable mixed moving averages. Their distribution determines a certain combination of the filter function and the mixing measure, leading to a generalization of a theorem of Kanter (1973) for usual moving averages. Stable mixed moving averages contain sums of independent stable moving averages, are ergodic and are not harmonizable. Also a class of stable mixed moving averages is constructed with the reflection positivity property.
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Research supported by AFSOR Contract 91-0030
Research also supported by ARO DAAL-91-G-0176
Research also supported by AFOSR 90-0168
Research also supported by ONR N00014-91-J-0277