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
XIV: 30, 255-255, LNM 784 (1980)
REBOLLEDO, Rolando
Corrections à ``Décomposition des martingales locales et raréfaction des sauts'' (
General theory of processes,
Martingale theory)
Concerns
1311. For the definitive version, see
Mém. Soc. Math. France, 62, 1979
Keywords: Central limit theorem,
Skorohod topology,
Local martingales,
JumpsNature: Correction Retrieve article from Numdam
XXIX: 26, 266-289, LNM 1613 (1995)
EISENBAUM, Nathalie
Une version sans conditionnement du théorème d'isomorphisme de Dynkin (
Limit theorems)
After establishing an unconditional version of Dynkin's isomorphism theorem, the author applies this theorem to give a new proof of Ray-Knight theorems for Brownian local times, and also to give another proof to limit theorems due to Rosen
2533 concerning the increments of the local times of a symmetric $\beta$-stable process for $\beta>1$. Some results by Marcus-Rosen (
Proc. Conf. Probability in Banach Spaces~8, Birkhäuser 1992) on Laplace transforms of the increments of local time are extended
Comment: A general reference on the subject is Marcus-Rosen,
Markov Processes, Gaussian Processes, and Local Times, Cambridge University Press (2006)
Keywords: Stable processes,
Local times,
Central limit theorem,
Dynkin isomorphism,
Fractional Brownian motion,
Brownian sheetNature: Original Retrieve article from Numdam
XXXI: 20, 216-224, LNM 1655 (1997)
EISENBAUM, Nathalie
Théorèmes limites pour les temps locaux d'un processus stable symétrique (
Limit theorems)
Using Dynkin's isomorphism, a central-limit type theorem is derived for the local times of a stable symmetric process of index $\beta$ at a finite number $n$ of levels. The limiting process is expressed in terms of a fractional, $n$-dimensional Brownian sheet with Hurst index $\beta-1$. The case when $n=1$ is due to Rosen
2533, and, for Brownian local times, to Yor
1709Comment: This kind of result is now understood as a weak form of theorems à la Ray-Knight, describing the local times of a stable symmetric process: see Eisenbaum-Kaspi-Marcus-Rosen-Shi
Ann. Prob. 28 (2000) for a Ray-Knight theorem involving fractional Brownian motion. Marcus-Rosen,
Markov Processes, Gaussian Processes, and Local Times, Cambridge University Press (2006) is a general reference on the subject
Keywords: Stable processes,
Local times,
Central limit theorem,
Dynkin isomorphism,
Fractional Brownian motion,
Brownian sheetNature: Original Retrieve article from Numdam
XLIII: 03, 95-104, LNM 2006 (2011)
ROSEN, Jay
A stochastic calculus proof of the CLT for the $L^{2}$ modulus of continuity of local time (
Theory of Brownian motion)
Keywords: Central Limit Theorem,
Moduli of continuity,
Local times,
Brownian motionNature: Original
XLV: 16, 401-431, LNM 2078 (2013)
NOREDDINE, Salim
Fluctuations of the Traces of Complex-Valued Random Matrices (
Non commutative probability theory)
Keywords: Random matrices,
Central limit theoremNature: Original
