Quick search | Browse volumes | |

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

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 logarithm

Nature: 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 laws

Nature: 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 paths

Nature: Original

Retrieve article from Numdam

Un théorème de Linnik (Independence)

The result proved (which implies that of Linnik mentioned in the title) is due to Ostrovskii (

Keywords: Infinitely divisible laws, Characteristic functions

Nature: Exposition

Retrieve article from Numdam

III: 07, 137-142, LNM 88 (1969)

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

Retrieve article from Numdam

VI: 01, 1-34, LNM 258 (1972)

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 $

Comment: The results were announced in the note

Keywords: Decomposition of laws

Nature: Original

Retrieve article from Numdam

XIII: 14, 174-198, LNM 721 (1979)

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, $

Keywords: Stopping points, Random increasing paths

Nature: Original

Retrieve article from Numdam