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VOL. 51 | 2006 Invariance principle for stochastic processes with short memory
Magda Peligrad, Sergey Utev

Editor(s) Evarist Giné, Vladimir Koltchinskii, Wenbo Li, Joel Zinn

## Abstract

In this paper we give simple sufficient conditions for linear type processes with short memory that imply the invariance principle. Various examples including projective criterion are considered as applications. In particular, we treat the weak invariance principle for partial sums of linear processes with short memory. We prove that whenever the partial sums of innovations satisfy the $L_{p}$--invariance principle, then so does the partial sums of its corresponding linear process.

## Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1122.60038
MathSciNet: MR2387758

Digital Object Identifier: 10.1214/074921706000000734

Subjects:
Primary: 60F17 , 60F17
Secondary: 60G10 , 60G48 , 60K99

Keywords: Brownian motion , invariance principle , linear processes , stationary process , weakly dependent sequences

Rights: Copyright © 2006, Institute of Mathematical Statistics

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Vol. 51 • 1 January 2006