STABLE MIXED MOVING AVERAGES

• 成果类型: Article
• 署名作者: SURGAILIS, D; ROSINSKI, J; MANDREKAR, V; CAMBANIS, S
• 署名单位: Vilnius University; University of Tennessee System; University of Tennessee Knoxville; Michigan State University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01192963
• 发表日期: 1993
• 页码: 543-558
• 关键词: spectral representation

摘要

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.