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4 matches found
II: 06, 111-122, LNM 51 (1968)
IGOT, Jean-Pierre
Un théorème de Linnik (Independence)
The result proved (which implies that of Linnik mentioned in the title) is due to Ostrovskii (Uspehi Mat. Nauk, 20, 1965) and states that the convolution of a normal and a Poisson law decomposes only into factors of the same type
Keywords: Infinitely divisible laws, Characteristic functions
Nature: Exposition
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III: 07, 137-142, LNM 88 (1969)
HUBER, Catherine
Un aspect de la loi du logarithme itéré pour des variables aléatoires indépendantes et équidistribuées (Independence)
A refinement of the classical law of the iterated logarithm for i.i.d. random variables, under regularity assumptions on the tail of the common distribution
Keywords: Law of the iterated logarithm
Nature: Original
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VI: 01, 1-34, LNM 258 (1972)
ARTZNER, Philippe
Echantillons et couples indépendants de points aléatoires portés par une surface convexe (Independence)
The general problem is to find conditions under which a convolution equation $\mu{*}\mu=\mu'{*}\mu''$ in $R^n$ implies that $\mu'=\mu''=\mu$. It is shown here that the result is true if the measures are carried by a convex surface which is not too flat
Comment: The results were announced in the note C. R. Acad. Sci., 272, 1971
Keywords: Decomposition of laws
Nature: Original
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XIII: 14, 174-198, LNM 721 (1979)
CAIROLI, Renzo; GABRIEL, Jean-Pierre
Arrêt de certaines suites multiples de variables aléatoires indépendantes (Several parameter processes, Independence)
Let $(X_n)$ be independent, identically distributed random variables. It is known that $X_T/T\in L^1$ for all stopping times $T$ (or the same with $S_n=X_1+...+X_n$ replacing $X_n$) if and only if $X\in L\log L$. The problem is to extend this to several dimensions, $N^d$ ($d>1$) replacing $N$. Then a stopping time $T$ becomes a stopping point, of which two definitions can be given (the past at time $n$ being defined either as the past rectangle, or the complement of the future rectangle), and $|T|$ being defined as the product of the coordinates). The appropriate space then is $L\log L$ or $L\log^d L$ depending on the kind of stopping times involved. Also the integrability of the supremum of the processes along random increasing paths is considered
Keywords: Stopping points, Random increasing paths
Nature: Original
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