XIV: 06, 53-61, LNM 784 (1980)
AZÉMA, Jacques;
GUNDY, Richard F.;
YOR, Marc
Sur l'intégrabilité uniforme des martingales exponentielles (
Martingale theory)
The main result of this paper is the following: Let $X$ be a martingale which is continuous and bounded in $L^1$ (both conditions are essential). Then $X$ is uniformly integrable if and only if $tP\{X^{*}>t\}$ or equivalently $tP\{S(X)>t\}$ tend to $0$ as $t\rightarrow\infty$, where $S(X)$ is the usual square function. The methods (using a good lambda inequality) are close to
1404Comment: Generalized by Takaoka
3313Keywords: Exponential martingales,
Continuous martingalesNature: Original
Retrieve article from Numdam
XVIII: 06, 77-81, LNM 1059 (1984)
GUNDY, Richard F.
Temps locaux et intégrale d'aire de Lusin Retrieve article from Numdam
