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3 matches found
XII: 17, 148-161, LNM 649 (1978)
LÉPINGLE, Dominique
Sur le comportement asymptotique des martingales locales (Martingale theory)
This paper is devoted to the extension of well-known statements (the strong law of large numbers, the Borel-Cantelli lemma, and the easier half of the law of the iterated logarithm) to right-continuous local martingales. An interesting technical point is the definition of a family of exponential supermartingales
Keywords: Law of large numbers, Borel-Cantelli lemma, Exponential martingales, Law of the iterated logarithm
Nature: Original
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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 1404
Comment: Generalized by Takaoka 3313
Keywords: Exponential martingales, Continuous martingales
Nature: Original
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XVI: 29, 338-347, LNM 920 (1982)
YAN, Jia-An
À propos de l'intégrabilité uniforme des martingales exponentielles (Martingale theory)
Sufficient conditions are given for the uniform integrability of the exponential ${\cal E}(M)$, where $M$ is a local martingale with jumps $\ge-1$, refining older results of Lépingle and Mémin, and of the author. They involve the Lévy measure of the martingale
Comment: In the lemma p.339 delete the assumption $0<\beta$
Keywords: Exponential martingales
Nature: Original
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