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 functionsNature: Exposition
Retrieve article from Numdam
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 logarithmNature: Original Retrieve article from Numdam
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 lawsNature: Original Retrieve article from Numdam
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 pathsNature: Original Retrieve article from Numdam
