Invariance principles and Gaussian approximation for strictly stationary processes

Author:
Dalibor Volný

Journal:
Trans. Amer. Math. Soc. **351** (1999), 3351-3371

MSC (1991):
Primary 28D05, 60G10, 60F17, 60F05, 28D20

DOI:
https://doi.org/10.1090/S0002-9947-99-02401-0

Published electronically:
April 8, 1999

MathSciNet review:
1624218

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that in any aperiodic and ergodic dynamical system there exists a square integrable process the partial sums of which can be closely approximated by the partial sums of Gaussian i.i.d. random variables. For both weak and strong invariance principles hold.

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Additional Information

**Dalibor Volný**

Affiliation:
Université de Rouen, UPRES-A CNRS 60 85, Site Colbert, 76821 Mont-Saint-Aignan Cedex, France

Email:
dalibor.volny@univ-rouen.fr

DOI:
https://doi.org/10.1090/S0002-9947-99-02401-0

Keywords:
Zero entropy stationary process,
weak invariance principle,
strong invariance principle,
approximation by Gaussian random variables

Received by editor(s):
February 21, 1997

Published electronically:
April 8, 1999

Additional Notes:
This research has been partially supported by the Grant Agency of the Charles University (Prague), grant #GAUK 6191

Article copyright:
© Copyright 1999
American Mathematical Society