Vector-valued decoupling and the Burkholder-Davis-Gundy inequality

Details Vector-valued decoupling and the Burkholder-Davis-Gundy inequality Vector-valued decoupling and the Burkholder-Davis-Gundy inequality

2011-07-12

arxiv.org/abs/1107.2218v1

Mathematics

Functional Analysis

To appear in the Illinois Journal of Mathematics

Scientific paper

Let X be a Banach space. We prove p-independence of the one-sided decoupling inequality for X-valued tangent martingales as introduced by Kwapien and Woyczynski. It is known that a Banach space X satisfies the two-sided decoupling inequality if and only if X is a UMD Banach space. The one-sided decoupling inequality is a weaker property, including e.g. the space L^1. We provide information on the optimal constants for various spaces, and give a upper estimate of order p in general. In the second part of our paper we derive Burkholder-Davis-Gundy type estimates for p-th moments, p in (0,infty), of X-valued stochastic integrals, provided X is a UMD Banach space or a space in which the one-sided decoupling inequality holds.

Affiliated with

Also associated with

No associations

Rating

Vector-valued decoupling and the Burkholder-Davis-Gundy inequality does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Vector-valued decoupling and the Burkholder-Davis-Gundy inequality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Vector-valued decoupling and the Burkholder-Davis-Gundy inequality will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-565155