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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

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 theorem

Nature: Original

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,

Keywords: Subsequences, Central limit theorem, Law of the iterated logarithm

Nature: Exposition

Retrieve article from Numdam

XIV: 30, 255-255, LNM 784 (1980)

Corrections à ``Décomposition des martingales locales et raréfaction des sauts'' (General theory of processes, Martingale theory)

Concerns 1311. For the definitive version, see

Keywords: Central limit theorem, Skorohod topology, Local martingales, Jumps

Nature: Correction

Retrieve article from Numdam

XXIX: 26, 266-289, LNM 1613 (1995)

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 (

Comment: A general reference on the subject is Marcus-Rosen,

Keywords: Stable processes, Local times, Central limit theorem, Dynkin isomorphism, Fractional Brownian motion, Brownian sheet

Nature: Original

Retrieve article from Numdam

XXXI: 20, 216-224, LNM 1655 (1997)

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

Keywords: Stable processes, Local times, Central limit theorem, Dynkin isomorphism, Fractional Brownian motion, Brownian sheet

Nature: Original

Retrieve article from Numdam

XLIII: 03, 95-104, LNM 2006 (2011)

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

XLV: 16, 401-431, LNM 2078 (2013)

Fluctuations of the Traces of Complex-Valued Random Matrices (Non commutative probability theory)

Keywords: Random matrices, Central limit theorem

Nature: Original