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arXiv · 2003.03598

Burkholder's function and a weighted $L^2$ bound for stochastic integrals

Rodrigo Banuelos·Michal Brzozowski·Adam Osekowski
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Abstract

Let $X$ be a continuous-path martingale and let $Y$ be a stochastic integral, with respect to $X$, of some predictable process with values in $[-1,1]$. We provide an explicit formula for Burkholder's function associated with the weighted $L^2$ bound $$ \|Y\|_{L^2(W)}\lesssim [w]_{A_2}\|X\|_{L^2(W)}.$$

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Rodrigo Banuelos, Michal Brzozowski, Adam Osekowski. 2020-03-07. Burkholder's function and a weighted $L^2$ bound for stochastic integrals. https://arxiv.org/abs/2003.03598

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