Sharp equivalence between ρ- and τ-mixing coefficients

• Autorzy: Rémi Peyre
• Języki publikacji: EN

Abstrakty

EN

For two σ-algebras 𝓐 and ℬ, the ρ-mixing coefficient ρ(𝓐,ℬ) between 𝓐 and ℬ is the supremum correlation between two real random variables X and Y which are 𝓐 - resp. ℬ-measurable; the τ'(𝓐,ℬ) coefficient is defined similarly, but restricting to the case where X and Y are indicator functions. It has been known for a long time that the bound ρ ≤ Cτ'(1 + en | log τ'|) holds for some constant C; in this article, we show that C = 1 works and is best possible.

Kategorie tematyczne

• 62H20: Measures of association (correlation, canonical correlation, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 216
• Numer: 3
• Strony: 245-270

Daty

wydano

2013

Twórcy

autor

Rémi Peyre

• Institut Élie Cartan, Université de Lorraine, 54506 Vandœuvre-lès-Nancy, France

Identyfikatory

DOI

10.4064/sm216-3-4