Tome (1991)

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

GDML_Books, (1991), p.

Abstract
Abstract

Let $τ_{n}, n \geq 0$ be a sequence of measure preserving transformations of a probability space (Ω,Σ,P) into itself and let $f_{n}, n \geq 0$ be a sequence of elements of $L^{2} (Ω, Σ, P)$ with $E f_{n} = 0$ . It is shown that the distribution of $(\sum_{i = 0}^{n} f_{i} \circ τ_{i} \circ . . . \circ τ_{0}) {(D (\sum_{i = 0}^{n} f_{i} \circ τ_{i} \circ . . . \circ τ_{0}))}^{- 1}$ tends to the normal distribution N(0,1) as n → ∞.

1985 Mathematics Subject Classification: 58F11, 60F05, 28D99.

CONTENTS1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52. A central limit theorem for martingale differences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83. Stationary family of processes and central limit theorems for its elements. . . . . . . . . . . . . . .164. Central limit theorems for processes determined by endomorphisms. . . . . . . . . . . . . . . . . . 235. The central limit theorems for automorphisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .466. Final remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61

Zbl 0744.60023

EUDML-ID : urn:eudml:doc:219350

@book{bwmeta1.element.zamlynska-4d448c64-afff-4f5c-a6d6-b126836300fa,
     author = {Marian Jab\l o\'nski},
     title = {A central limit theorem for processes generated by a family of transformations},
     series = {GDML\_Books},
     publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
     address = {Warszawa},
     year = {1991},
     zbl = {0744.60023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-4d448c64-afff-4f5c-a6d6-b126836300fa}
}

Marian Jabłoński. A central limit theorem for processes generated by a family of transformations. GDML_Books (1991),  http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-4d448c64-afff-4f5c-a6d6-b126836300fa/