On quotients of moving average processes with infinite mean
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- by Marek Kanter
- Proc. Amer. Math. Soc. 56 (1976), 281-287
- DOI: https://doi.org/10.1090/S0002-9939-1976-0402890-1
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Erratum: Proc. Amer. Math. Soc. 67 (1977), 362.
Abstract:
In this paper it is shown that one can estimate the sum of the weights used to form a stationary moving average stochastic process based on nonnegative random variables by taking the limit in probability of suitable quotients, even when the random variables involved have infinite expectation.References
- Leo Breiman, Probability, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1968. MR 0229267
- Harald Cramér and M. R. Leadbetter, Stationary and related stochastic processes. Sample function properties and their applications, John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR 0217860
- William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, at the University Press, 1952. 2d ed. MR 0046395
- Marek Kanter and W. L. Steiger, Regression and autoregression with infinite variance, Advances in Appl. Probability 6 (1974), 768–783. MR 365963, DOI 10.2307/1426192 J. Keilson, Green’s function methods in probability theory, Griffin’s Statistical Monographs and Courses, no. 17, Hafner, New York, 1965. MR 34 #2063. P. Lévy, Théorie de l’addition des variables aléatoires, 2nd ed., Gauthier-Villars, Paris, 1954.
- Michel Loève, Probability theory, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-New York-London, 1960. 2nd ed. MR 0123342
- H. D. Miller, A note on sums of independent random variables with infinite first moment, Ann. Math. Statist. 38 (1967), 751–758. MR 211445, DOI 10.1214/aoms/1177698868
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 281-287
- MSC: Primary 60G10; Secondary 62M10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0402890-1
- MathSciNet review: 0402890