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

DOI:
https://doi.org/10.1090/S0002-9939-98-04177-X

MathSciNet review:
1425136

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-98-04177-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