Two Inequalities for the First Moments of a Martingale, its Square Function and its Maximal Function

• Autorzy: Adam Osękowski
• Języki publikacji: EN

Abstrakty

EN

Given a Hilbert space valued martingale (Mₙ), let (M*ₙ) and (Sₙ(M)) denote its maximal function and square function, respectively. We prove that
𝔼|Mₙ| ≤ 2𝔼 Sₙ(M), n=0,1,2,...,
𝔼 M*ₙ ≤ 𝔼 |Mₙ| + 2𝔼 Sₙ(M), n=0,1,2,....
The first inequality is sharp, and it is strict in all nontrivial cases.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: 53
• Numer: 4
• Strony: 441-449

Daty

wydano

2005

Twórcy

autor

Adam Osękowski

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba53-4-9