Wyniki wyszukiwania

1

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

100%

Jabłoński M.

Instytut Matematyczny Polskiej Akademii Nauk

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 → ∞.

XX

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

2

On a gap series of Mark Kac

98%

Fukuyama K.

Colloquium Mathematicum

|

1999

|

tom 81

|

nr 2

157-160

EN

Mark Kac gave an example of a function f on the unit interval such that f cannot be written as f(t)=g(2t)-g(t) with an integrable function g, but the limiting variance of $n^{-1/2}\sum_{k=0}^{n-1} f(2^kt)$ vanishes. It is proved that there is no measurable g such that f(t)=g(2t)-g(t). It is also proved that there is a non-measurable g which satisfies this equality.

3

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Limit distributions of extreme order statistics

98%

Dziubdziela W.

Mathematica Applicanda

|

1977

|

tom 5

|

nr 9

PL

Artykuł nie zawiera streszczenia

EN

MR0482946

4

On the universal constant in the Katz-Petrov and Osipov inequalities

86%

Korolev V., Popov S.

Discussiones Mathematicae Probability and Statistics

|

2011

|

tom 31

|

nr 1-2

29-39

EN

Upper estimates are presented for the universal constant in the Katz-Petrov and Osipov inequalities which do not exceed 3.1905.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Discussiones Mathematicae Probability and Statistics

1 Mathematica Applicanda

1 Dziubdziela W.

1 Fukuyama K.

1 Jabłoński M.

1 Korolev V.

1 Popov S.

1 2011

1 1999

1 1991

1 1977

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

On a gap series of Mark Kac

Limit distributions of extreme order statistics

On the universal constant in the Katz-Petrov and Osipov inequalities