# A central limit theorem for processes generated by a family of transformations

• Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1991

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## Abstract

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Let ${\tau }_{n},n\ge 0$ be a sequence of measure preserving transformations of a probability space (Ω,Σ,P) into itself and let ${f}_{n},n\ge 0$ be a sequence of elements of ${L}^{2}\left(\Omega ,\Sigma ,P\right)$ with $E{f}_{n}=0$. It is shown that the distribution of$\left({\sum }_{i=0}^{n}{f}_{i}\circ {\tau }_{i}\circ ...\circ {\tau }_{0}\right){\left(D\left({\sum }_{i=0}^{n}{f}_{i}\circ {\tau }_{i}\circ ...\circ {\tau }_{0}\right)\right)}^{-1}$tends to the normal distribution N(0,1) as n → ∞.1985 Mathematics Subject Classification: 58F11, 60F05, 28D99.

## How to cite

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Marian Jabłoński. A central limit theorem for processes generated by a family of transformations. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1991. <http://eudml.org/doc/219350>.

@book{MarianJabłoński1991,
abstract = {Let $\{τ_n,n≥0\}$ be a sequence of measure preserving transformations of a probability space (Ω,Σ,P) into itself and let $\{f_n,n≥0\}$ be a sequence of elements of $L^2(Ω,Σ,P)$ with $E\{f_n\}=0$. It is shown that the distribution of$(∑_\{i=0\}^\{n\}f_i∘τ_i∘...∘τ_0)(D(∑_\{i=0\}^nf_i∘τ_i∘...∘τ_0))^\{-1\}$tends to the normal distribution N(0,1) as n → ∞.1985 Mathematics Subject Classification: 58F11, 60F05, 28D99.},
author = {Marian Jabłoński},
keywords = {conditional expectation; martingale differences; central limit theorem; ergodic, mixing and exact transformations.; ergodic; mixing; measure preserving transformations},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {A central limit theorem for processes generated by a family of transformations},
url = {http://eudml.org/doc/219350},
year = {1991},
}

TY - BOOK
AU - Marian Jabłoński
TI - A central limit theorem for processes generated by a family of transformations
PY - 1991
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - Let ${τ_n,n≥0}$ be a sequence of measure preserving transformations of a probability space (Ω,Σ,P) into itself and let ${f_n,n≥0}$ be a sequence of elements of $L^2(Ω,Σ,P)$ with $E{f_n}=0$. It is shown that the distribution of$(∑_{i=0}^{n}f_i∘τ_i∘...∘τ_0)(D(∑_{i=0}^nf_i∘τ_i∘...∘τ_0))^{-1}$tends to the normal distribution N(0,1) as n → ∞.1985 Mathematics Subject Classification: 58F11, 60F05, 28D99.
LA - eng
KW - conditional expectation; martingale differences; central limit theorem; ergodic, mixing and exact transformations.; ergodic; mixing; measure preserving transformations
UR - http://eudml.org/doc/219350
ER -

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