Gebelein's inequality and its consequences

• Autorzy: M. Beśka , Z. Ciesielski
• Języki publikacji: EN

Abstrakty

EN

Let $(X_i, i=1,2,...)$ be the normalized gaussian system such that $X_i ∈ N(0,1)$, i = 1,2,... and let the correlation matrix $ρ_{ij} = E(X_iX_j)$ satisfy the following hypothesis:
$C = sup_{i≥1} ∑_{j=1}^{∞} |ρ_{i,j}| < ∞$.
We present Gebelein's inequality and some of its consequences: Borel-Cantelli type lemma, iterated log law, Levy's norm for the gaussian sequence etc. The main result is that
(f(X₁) + ⋯ + f(Xₙ))/n → 0 a.s.
for f ∈ L¹(ν) with (f,1)_ν = 0.

Kategorie tematyczne

• 60F15: Strong theorems
• 60F20: Zero-one laws
• 47B34: Kernel operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 72
• Numer: 1
• Strony: 11-23

Daty

wydano

2006

Twórcy

autor

M. Beśka

• Faculty of Applied Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-952 Gdańsk, Poland

autor

Z. Ciesielski

• Institute of Mathematics, Polish Academy of Sciences, Abrahama 18, 81-125 Sopot, Poland

Identyfikatory

DOI

10.4064/bc72-0-1