Abstract: For an automorphisms with non-zero Kolmogorov-Sinai entropy, a new class of L2-functions called the Gordin space is considered. This space is the linear span of Gordin classes constructed by some automorphism-invariant filtration of σ-algebras Fn. A function from the Gordin class is an orthogonal projection with respect to the operator I −E(·|Fn) of some Fm-measurable function. After Gordin’s work on the use of the martingale method to prove the central limit theorem, this construction was developed in the works of Voln´y. In this review article we consider this construction in ergodic theory. It is shown that the rate of convergence of ergodic averages in the L2 norm for functions from the Gordin space is simply calculated and is O( 1 √n ). It is also shown that the Gordin space is a dense set of the first Baire category in L2(Ω,F,µ) ⊖ L2(Ω,Π(T,F),µ), where Π(T,F) is the Pinsker σ-algebra.

Cite: Podvigin I.V.
On the rate of convergence of ergodic averages for functions of Gordin space
Владикавказский математический журнал (Vladikavkaz Mathematical Journal). 2024. V.26. N2. P.95-102. DOI: 10.46698/w0408-5668-5674-e Scopus РИНЦ OpenAlex

Dates:

Submitted:	Dec 21, 2023
Published print:	Jun 30, 2024
Published online:	Jun 30, 2024

Identifiers:

Scopus:	2-s2.0-85198133117
Elibrary:	67950170
OpenAlex:	W4399976479

Citing: Пока нет цитирований

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