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- Publisher
- Springer Basel
- Copyright
- © Springer Basel 2013
- ISBN
- 978-3-0348-0489-9
- Pages
- 113 –138
- DOI
- 10.1007/978-3-0348-0490-5_9
- Publisher site
- See Chapter on Publisher Site
Abstract
[In this paper, we give rates of convergence in the strong invariance principle for non-adapted sequences satisfying projective criteria. The results apply to the iterates of ergodic automorphisms T of the d-dimensional torus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{T}^d$$ \end{document}, even in the non hyperbolic case. In this context, we give a large class of unbounded function f from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{T}^d$$ \end{document} to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{R}$$ \end{document}, for which the partial sum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$f\;\circ\;T\;+\;f\;\circ\;T^{2}\;+\;.\;.\;.\;+\;f\;\circ\;T^{n}$$ \end{document} satisfies a strong invariance principle with an explicit rate of convergence.]
Published: Apr 1, 2013
Keywords: Almost sure invariance principle; strong approximations; nonadapted sequences; ergodic automorphisms of the torus