On quotients of moving average processes with infinite mean

Author:
Marek Kanter

Journal:
Proc. Amer. Math. Soc. **56** (1976), 281-287

MSC:
Primary 60G10; Secondary 62M10

Erratum:
Proc. Amer. Math. Soc. **67** (1977), 362.

MathSciNet review:
0402890

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

**[1]**Leo Breiman,*Probability*, Addison-Wesley Publishing Company, Reading, Mass.-London-Don Mills, Ont., 1968. MR**0229267****[2]**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****[3]**William Feller,*An introduction to probability theory and its applications. Vol. II*, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR**0210154****[4]**G. H. Hardy, J. E. Littlewood, and G. Pólya,*Inequalities*, Cambridge, at the University Press, 1952. 2d ed. MR**0046395****[5]**Marek Kanter and W. L. Steiger,*Regression and autoregression with infinite variance*, Advances in Appl. Probability**6**(1974), 768–783. MR**0365963****[6]**J. Keilson,*Green's function methods in probability theory*, Griffin's Statistical Monographs and Courses, no. 17, Hafner, New York, 1965. MR**34**#2063.**[7]**P. Lévy,*Théorie de l'addition des variables aléatoires*, 2nd ed., Gauthier-Villars, Paris, 1954.**[8]**Michel Loève,*Probability theory*, 2nd ed. The University Series in Higher Mathematics. D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-New York-London, 1960. MR**0123342****[9]**H. D. Miller,*A note on sums of independent random variables with infinite first moment*, Ann. Math. Statist.**38**(1967), 751–758. MR**0211445**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
60G10,
62M10

Retrieve articles in all journals with MSC: 60G10, 62M10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1976-0402890-1

Keywords:
Moving average process,
stationary process,
ergodic theorems,
quotients of independent random variables,
metric linear space

Article copyright:
© Copyright 1976
American Mathematical Society