Some new Bellman functions and subordination by orthogonal martingales in $L^{p}, 1<p\le 2$

Details Some new Bellman functions and subordination by orthogonal martingales in $L^{p}, 1<p\le 2$ Some new Bellman functions and subordination by orthogonal martingales in $L^{p}, 1<p\le 2$

2010-12-04

arxiv.org/abs/1012.0947v1

Mathematics

Probability

32 pages

Scientific paper

Given two martingales on the filtration generated by two dimensional Brownian motion, we want to estimate the $L^p$ norm of the subordinated one if we have some extra orthogonality property available. We construct several new Bellman functions, very different from Burkholder's function, and using them give an estimate of $L^p$ norm of a subordinated martingale, if the dominating martingale is orthogonal and $1

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