On the Almost Sure Central Limit Theorem for a Class of Z d -Actions

Mikhail Gordin () and Michel Weber ()
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Mikhail Gordin: V. A. Steklov Mathematical Institute at St Petersburg
Michel Weber: Université Louis-Pasteur

Journal of Theoretical Probability, 2002, vol. 15, issue 2, 477-501

Abstract: Abstract As an extension of earlier papers on stationary sequences, a concept of weak dependence for strictly stationary random fields is introduced in terms of so-called homoclinic transformations. Under assumptions made within the framework of this concept a form of the almost sure central limit theorem (ASCLT) is established for random fields arising from a class of algebraic Z d -actions on compact abelian groups. As an auxillary result, the central limit theorem is proved via Ch. Stein's method. The next stage of the proof includes some estimates which are specific for ASCLT. Both steps are based on making use of homoclinic transformations.

Keywords: Hilbert spaces; Z d -actions; weighted series; almost sure convergence (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1015014927939

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