Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On quotients of moving average processes with infinite mean
HTML articles powered by AMS MathViewer

by Marek Kanter PDF
Proc. Amer. Math. Soc. 56 (1976), 281-287 Request permission

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60G10, 62M10
  • Retrieve articles in all journals with MSC: 60G10, 62M10
Additional 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