STABLE MIXED MOVING AVERAGES

被引：40
作者：
SURGAILIS, D
ROSINSKI, J
MANDREKAR, V
CAMBANIS, S
机构：
[1] LITHUANIA ACAD SCI, INST MATH & INFORMAT, 2600 VILNIUS, LITHUANIA
[2] UNIV TENNESSEE, DEPT MATH, KNOXVILLE, TN 37996 USA
[3] MICHIGAN STATE UNIV, DEPT STAT & PROBABIL, E LANSING, MI 48824 USA
来源：
PROBABILITY THEORY AND RELATED FIELDS | 1993年 / 97卷 / 04期
关键词：
D O I：
10.1007/BF01192963
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
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页码：543 / 558
页数：16
相关论文
共 11 条
[1]   ON STABLE MARKOV-PROCESSES [J].
ADLER, RJ ;
CAMBANIS, S ;
SAMORODNITSKY, G .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1990, 34 (01) :1-17
[2]   ERGODIC PROPERTIES OF STATIONARY STABLE PROCESSES [J].
CAMBANIS, S ;
HARDIN, CD ;
WERON, A .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1987, 24 (01) :1-18
[3]  
Dunford N., 1988, LINEAR OPERATORS 1
[4]   ON THE SPECTRAL REPRESENTATION OF SYMMETRIC STABLE PROCESSES [J].
HARDIN, CD .
JOURNAL OF MULTIVARIATE ANALYSIS, 1982, 12 (03) :385-401
[5]   L-P NORM OF SUMS OF TRANSLATES OF A FUNCTION [J].
KANTER, M .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 179 (MAY) :35-47
[6]   GAUSSIAN OS-POSITIVE PROCESSES [J].
KLEIN, A .
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1977, 40 (02) :115-124
[7]   GENERALIZATION OF MARKOV-PROCESSES [J].
KLEIN, A .
ANNALS OF PROBABILITY, 1978, 6 (01) :128-132
[8]   THE SPECTRAL REPRESENTATION OF STABLE PROCESSES - HARMONIZABILITY AND REGULARITY [J].
MAKAGON, A ;
MANDREKAR, V .
PROBABILITY THEORY AND RELATED FIELDS, 1990, 85 (01) :1-11
[9]  
Meyer Paul-Andre., 1982, SEMINAIRE PROBABILIT, V920, P95
[10]  
Parthasarathy K. R., 1972, LECT NOTES MATH, V272
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