XXIX: 25, 260-265, LNM 1613 (1995)
EISENBAUM, Nathalie;
KASPI, Haya
A counterexample for the Markov property of local time for diffusions on graphs
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
XXXIII: 26, 417-418, LNM 1709 (1999)
EISENBAUM, Nathalie
Quelques précisions sur ``Théorèmes limites pour les temps locaux d'un processus stable symétrique'' (Volume XXXI, LNM. 1655, 1997) Retrieve article from Numdam
XXXIV: 02, 146-150, LNM 1729 (2000)
EISENBAUM, Nathalie
Exponential inequalities for Bessel processes Retrieve article from Numdam
XXXV: 22, 329-333, LNM 1755 (2001)
EISENBAUM, Nathalie
Occupation times of Lévy processes as quadratic variations Retrieve article from Numdam
XXXV: 26, 390-395, LNM 1755 (2001)
EISENBAUM, Nathalie
On Ito's formula of Föllmer and Protter Retrieve article from Numdam
XXXV: 29, 421-425, LNM 1755 (2001)
EISENBAUM, Nathalie
Are squared Bessel bridges infinitely divisible Retrieve article from Numdam
XXXVI: 13, 331-334, LNM 1801 (2003)
EISENBAUM, Nathalie
A Gaussian sheet connected to symmetric Markov chains
XXXVIII: 19, 282-289, LNM 1857 (2005)
EISENBAUM, Nathalie;
TUDOR, Ciprian A.
On squared fractional Brownian motions
XL: 06, 137-146, LNM 1899 (2007)
EISENBAUM, Nathalie
Local time-space calculus for reversible semimartingales
XLIV: 10, 207-213, LNM 2046 (2012)
EISENBAUM, Nathalie
Another failure in the analogy between Gaussian and semicircle laws (
Non commutative probability theory)
Keywords: Gaussian law,
Semicircle law,
Free Poisson distribution,
Free probability,
Free convolution,
$R$-transform,
Dynkin isomorphismNature: Original
