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July, 1995 Controle de la Norme $H^p$ D'Une Martingale par des Maximums de Temps Locaux
Christophe Leuridan
Ann. Probab. 23(3): 1289-1299 (July, 1995). DOI: 10.1214/aop/1176988184

Abstract

Let $B$ be a brownian motion starting at 0. We denote by $L^\ast_t = \max_{x\in\mathbb{R}} L^\ast_t$ the maximum of local times at time $t$. The Barlow-Yor inequalities tell us that for every $p > 0$, there are constants $C_p > c_p > 0$ such that for every stopping time $\tau$, $c_p\mathbb{E}\lbrack\tau^{p/2}\rbrack \leq \mathbb{E}\lbrack L^{\ast p}_\tau\rbrack \leq C_p\mathbb{E}\lbrack\tau^{p/2}\rbrack.$ Given a fixed closed set $F \subset \mathbb{R}$, we give a condition on $F$ which is necessary and sufficient to derive similar inequalities with $\max_{x\in F}L^x_\tau$ instead of $L^\ast_\tau$ and we prove various related results.

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Christophe Leuridan. "Controle de la Norme $H^p$ D'Une Martingale par des Maximums de Temps Locaux." Ann. Probab. 23 (3) 1289 - 1299, July, 1995. https://doi.org/10.1214/aop/1176988184

Information

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

zbMATH: 0833.60049
MathSciNet: MR1349172
Digital Object Identifier: 10.1214/aop/1176988184

Subjects:
Primary: 60G44
Secondary: 60J55 , 60J65

Keywords: $H^p$ norms , Brownian motion , Local times , Martingales , maximums of local times

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 3 • July, 1995
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