Browse by: Author name - Classification - Keywords - Nature

5 matches found
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 logarithm
Nature: Exposition
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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, Jumps
Nature: Correction
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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 sheet
Nature: Original
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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 1709
Comment: 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 sheet
Nature: Original
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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 motion
Nature: Original