Burkholder's submartingales from a stochastic calculus perspective
Probability
2007-05-25 v1
Abstract
We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in terms of a squared Brownian motion and of some appropriate powers of its maximum. Our techniques involve elementary stochastic calculus, as well as the Doob-Meyer decomposition of continuous submartingales. These results can be used to obtain an explicit expression of the constants appearing in the Burkholder-Davis-Gundy inequalities. A connection with some balayage formulae is also established.
Keywords
Cite
@article{arxiv.0705.3633,
title = {Burkholder's submartingales from a stochastic calculus perspective},
author = {Giovanni Peccati and Marc Yor},
journal= {arXiv preprint arXiv:0705.3633},
year = {2007}
}