A Note on the Burkholder-Rosenthal Inequality

• Autorzy: Adam Osękowski
• Języki publikacji: EN

Abstrakty

EN

Let df be a Hilbert-space-valued martingale difference sequence. The paper is devoted to a new, elementary proof of the estimate
$∥∑_{k=0}^{∞} df_k∥_p ≤ C_p {∥(∑_{k=0}^{∞} 𝔼 (|df_k|²| ℱ_{k-1}))^{1/2}∥_p + ∥(∑_{k=0}^{∞} |df_k|^p)^{1/p}∥_p},$
with $C_p = O(p/lnp)$ as p → ∞.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: 60
• Numer: 2
• Strony: 177-185

Daty

wydano

2012

Twórcy

autor

Adam Osękowski

• Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba60-2-7