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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Maximum of partial sums
and an invariance principle
for a class of weak dependent random variables


Author: Magda Peligrad
Journal: Proc. Amer. Math. Soc. 126 (1998), 1181-1189
MSC (1991): Primary 60F15, 60E15, 60G10
MathSciNet review: 1425136
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Abstract: The aim of this paper is to investigate the properties of the maximum of partial sums for a class of weakly dependent random variables which includes the instantaneous filters of a Gaussian sequence having a positive continuous spectral density. The results are used to obtain an invariance principle and the convergence of the moments in the central limit theorem.


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Additional Information

Magda Peligrad
Affiliation: Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221-0025
Email: peligrm@math.uc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04177-X
PII: S 0002-9939(98)04177-X
Keywords: Maximal inequalities, functional central limit theorem, weak dependent random variables
Received by editor(s): June 3, 1996
Received by editor(s) in revised form: October 7, 1996
Additional Notes: The author was supported in part by an NSF grant and cost sharing at the University of Cincinnati and a Tuft travel grant
Communicated by: Stanley Sawyer
Article copyright: © Copyright 1998 American Mathematical Society