Subordination by orthogonal martingales in L^p, 1

2010/12/04 by Prabhu Janakiraman, Alexander Volberg, Janakiraman, Prabhu +1
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Advanced Harmonic Analysis Research #Financial Risk and Volatility Modeling

paper · pdf · doi:10.48550/arxiv.1012.0948

Abstract

We are given two martingales on the filtration of the two dimensional Brownian motion. One is subordinated to another. We want to give an estimate of L^p-norm of a subordinated one via the same norm of a dominating one. In this setting this was done by Burkholder in \citeBu1--\citeBu8. If one of the martingales is orthogonal, the constant should drop. This was demonstrated in \citeBaJ1, when the orthogonality is attached to the subordinated martingale and when 2≤ p

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