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: 04, 72-89, LNM 258 (1972)
CHATTERJI, Shrishti Dhav
Un principe de sous-suites dans la théorie des probabilités (
Measure theory)
This paper is devoted to results of the following kind: any sequence of random variables with a given weak property contains a subsequence which satisfies a stronger property. An example is due to Komlós: any sequence bounded in $L^1$ contains a subsequence which converges a.s. in the Cesaro sense. Several results of this kind, mostly due to the author, are presented without detailed proofs
Comment: See
1302 for extensions to the case of Banach space valued random variables. See also Aldous,
Zeit. für W-theorie, 40, 1977
Keywords: Subsequences,
Central limit theorem,
Law of the iterated logarithmNature: Exposition Retrieve article from Numdam
VIII: 10, 134-149, LNM 381 (1974)
KNIGHT, Frank B.
Existence of small oscillations at zeros of brownian motion (
Brownian motion)
The one-dimensional Brownian motion path is shown to have an abnormal behaviour (an ``iterated logarithm'' upper limit smaller than one) at uncountably many times on his set of zeros
Comment: This result may be compared to Kahane,
C.R. Acad. Sci. 248, 1974
Keywords: Law of the iterated logarithm,
Local timesNature: Original Retrieve article from Numdam
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 logarithmNature: Original Retrieve article from Numdam
XV: 03, 11-37, LNM 850 (1981)
LEDOUX, Michel
La loi du logarithme itéré bornée dans les espaces de Banach (
Banach space valued random variables)
To be completed
Keywords: Law of the iterated logarithmNature: Original Retrieve article from Numdam
XLV: 10, 277-300, LNM 2078 (2013)
DONEY, R. A.;
VAKEROUDIS, S.
Windings of Planar Stable Processes (
Theory of processes)
Keywords: Stable processes,
Lévy processes,
Brownian motion,
windings,
exit time from a cone,
Spitzer's Theorem,
skew-product representation,
Lamperti's relation,
Law of the Iterated Logarithm for small timesNature: Original
