Non uniform averages in ergodic theorem for stochastic flows

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Non uniform averages in ergodic theorem for stochastic flows

Doklady Mathematics. 2009. Vol. 432. No. 4. P. 439–442.

Королев А. В., Bogachev V., Пилипенко А. Ю.

The paper deals with studying of convergence for non uniform averaging of the Kozlov-Treschev type for ergodic diffusion processes generated by stochastic differential equations. Korolev A.V. has proved the convergence result.

Language: English

Keywords: ergodic theorem

Convergence of spherical averages for actions of Fuchsian groups

Bufetov A., Klimenko A. V., Series C., Commentarii Mathematici Helvetici 2023 Vol. 98 No. 1 P. 41–134

We prove pointwise convergence of spherical averages for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen–Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving ...

Added: February 29, 2024

Convergence of spherical averages for actions of Fuchsian Groups

Klimenko A. V., Bufetov A., Series C., / Series math "arxiv.org". 2018. No. 1805.11743.

Pointwise convergence of spherical averages is proved for a measure-preserving action of a Fuchsian group. The proof is based on a new variant of the Bowen-Series symbolic coding for Fuchsian groups that, developing a method introduced by Wroten, simultaneously encodes all possible shortest paths representing a given group element. The resulting coding is self-inverse, giving ...

Added: September 18, 2018

Теорема существования предельных кривых для полиномиальных адических автоморфизмов.

Minabutdinov A., Записки научных семинаров ПОМИ РАН 2016 Т. 448 С. 177–200

We prove existence of limiting curves (describing deviations in ergodic theorem) for cylindrical functions for Polynomial adic systems. For a general ergodic measure-preserving transformation and a summable function we give necessary condition of a limiting curve to exist. Our work generalizes results by E'. Janvresse, T. de la Rue and Y. Velenik. ...

Added: October 14, 2016