Sharp moment inequalities for differentially subordinated martingales

• Autorzy: Adam Osękowski
• Języki publikacji: EN

Abstrakty

EN

We determine the optimal constants $C_{p,q}$ in the moment inequalities
$||g||_{p} ≤ C_{p,q} ||f||_{q}$, 1 ≤ p< q< ∞,
where f = (fₙ), g = (gₙ) are two martingales, adapted to the same filtration, satisfying
|dgₙ| ≤ |dfₙ|, n = 0,1,2,...,
with probability 1. Furthermore, we establish related sharp estimates
||g||₁ ≤ supₙ𝔼Φ(|fₙ|) + L(Φ),
where Φ is an increasing convex function satisfying certain growth conditions and L(Φ) depends only on Φ.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 201
• Numer: 2
• Strony: 103-131

Daty

wydano

2010

Twórcy

autor

Adam Osękowski

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

Identyfikatory

DOI

10.4064/sm201-2-1