A Weak-Type Inequality for Submartingales and Itô Processes

• Autorzy: Adam Osękowski
• Języki publikacji: EN

Abstrakty

EN

Let α ∈ [0,1] be a fixed parameter. We show that for any nonnegative submartingale X and any semimartingale Y which is α-subordinate to X, we have the sharp estimate
$∥Y∥_{W} ≤ (2(α+1)²)/(2α+1) ∥X∥_{L^∞}$.
Here W is the weak-$L^∞$ space introduced by Bennett, DeVore and Sharpley. The inequality is already sharp in the context of α-subordinate Itô processes.

Kategorie tematyczne

• 60G42: Martingales with discrete parameter
• 60G44: Martingales with continuous parameter

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2015
• Tom: 63
• Numer: 1
• Strony: 73-88

Daty

wydano

2015

Twórcy

autor

Adam Osękowski

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

Identyfikatory

DOI

10.4064/ba63-1-9