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April, 1995 Differential Subordination and Strong Differential Subordination for Continuous-Time Martingales and Related Sharp Inequalities
Gang Wang
Ann. Probab. 23(2): 522-551 (April, 1995). DOI: 10.1214/aop/1176988278

Abstract

Let $X$ and $Y$ be two continuous-time martingales. If quadratic variation of $X$ minus that of $Y$ is a nondecreasing and nonnegative function of time, we say that $Y$ is differentially subordinate to $X$ and prove that $\|Y\|_p \leq (p^\ast - 1)\|X\|_p$ for $1 < p < \infty$, where $p^\ast = p \vee q$ and $q$ is the conjugate of $p$. This inequality contains Burkholder's $L^p$-inequality for stochastic integrals, which implies that the above inequality is sharp. We also extend his concept of strong differential subordination and several other of his inequalities, and sharpen an inequality of Banuelos.

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Gang Wang. "Differential Subordination and Strong Differential Subordination for Continuous-Time Martingales and Related Sharp Inequalities." Ann. Probab. 23 (2) 522 - 551, April, 1995. https://doi.org/10.1214/aop/1176988278

Information

Published: April, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0832.60055
MathSciNet: MR1334160
Digital Object Identifier: 10.1214/aop/1176988278

Subjects:
Primary: 60G44
Secondary: 60G42 , 60G46

Keywords: Differential subordination , martingale , sharp inequalities , strong differential subordination , submartingale

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 2 • April, 1995
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