## Electronic Journal of Probability

### Rates of convergence in the strong invariance principle under projective criteria

#### Abstract

We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our results apply to a large variety of examples. We present some applications to a reversible Markov chain, to symmetric random walks on the circle, and to functions of dependent sequences.

#### Article information

Source
Electron. J. Probab., Volume 17 (2012), paper no. 16, 31 pp.

Dates
Accepted: 28 February 2012
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465062338

Digital Object Identifier
doi:10.1214/EJP.v17-1849

Mathematical Reviews number (MathSciNet)
MR2900457

Zentralblatt MATH identifier
1245.60040

Subjects
Primary: 60F17: Functional limit theorems; invariance principles

Rights

#### Citation

Dedecker, Jérôme; Doukhan, Paul; Merlevède, Florence. Rates of convergence in the strong invariance principle under projective criteria. Electron. J. Probab. 17 (2012), paper no. 16, 31 pp. doi:10.1214/EJP.v17-1849. https://projecteuclid.org/euclid.ejp/1465062338

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