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

Seria
Rozprawy Matematyczne tom/nr w serii: 307 wydano: 1991
Zawartość
Warianty tytułu
Abstrakty
EN

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 → ∞.

CONTENTS
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. A central limit theorem for martingale differences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3. Stationary family of processes and central limit theorems for its elements. . . . . . . . . . . . . . .16
4. Central limit theorems for processes determined by endomorphisms. . . . . . . . . . . . . . . . . . 23
5. The central limit theorems for automorphisms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46
6. Final remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .57
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 307
Liczba stron
62
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCVII
Daty
wydano
1991
otrzymano
1989-05-24
poprawiono
1990-05-24
Twórcy
  • Institute of Informatics, Jagiellonian University, Kraków, Poland
Bibliografia
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  • [21] J. Rousseau-Egele, Un théorème de la limite locale pour une classe de transformations dilatantes, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), 305-308.
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Języki publikacji
EN
Uwagi
1985 Mathematics Subject Classification: 58F11, 60F05, 28D99.
Identyfikator YADDA
bwmeta1.element.zamlynska-4d448c64-afff-4f5c-a6d6-b126836300fa
Identyfikatory
ISBN
83-85116-07-9
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

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