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The brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices is interpreted as a system of interacting brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). We prove that a limiting...
The Brownian motion model introduced by Dyson [7] for the eigenvalues of
unitary random matrices N x N is interpreted as a system of N interacting
Brownian particles on the circle with electrostatic inter-particles
repulsion. The aim of this paper is to define the finite
particle system in a general setting including collisions between
particles. Then, we study the behaviour of this system when
the number of particles N goes to infinity (through the empirical
measure
process). We prove...
Limiting laws, as t→∞, for brownian motion penalised by the longest length of excursions up to t, or up to the last zero before t, or again, up to the first zero after t, are shown to exist, and are characterized.
In this paper, we prove some central and non-central limit theorems for renormalized weighted power variations of order q≥2 of the fractional brownian motion with Hurst parameter H∈(0, 1), where q is an integer. The central limit holds for 1/2q<H≤1−1/2q, the limit being a conditionally gaussian distribution. If H<1/2q we show the convergence in L2 to a limit which only depends on the fractional brownian motion, and if H>1−1/2q we show the convergence in L2 to a stochastic integral...
We study the question of the law of large numbers and central limit theorem for an additive functional of a Markov processes taking values in a Polish space that has Feller property under the assumption that the process is asymptotically contractive in the Wasserstein metric.
We prove the central limit theorem for symmetric diffusion processes with non-zero drift in a random environment. The case of zero drift has been investigated in e.g. [18], [7]. In addition we show that the covariance matrix of the limiting Gaussian random vector corresponding to the diffusion with drift converges, as the drift vanishes, to the covariance of the homogenized diffusion with zero drift.
A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.
A sample of i.i.d. continuous time Markov chains being
defined, the sum over each component of a real function of the
state is considered. For this functional, a central limit theorem
for the first hitting time of a prescribed level is proved.
The result extends the classical central limit theorem for order statistics.
Various reliability models are presented as examples of applications.
We consider a sequence of stochastic processes with continuous trajectories and we show conditions for the tightness of the sequence in the Hölder space with a parameter .
Random measures derived from a stationary process of compact subsets of the Euclidean space are introduced and the corresponding central limit theorem is formulated. The result does not require the Poisson assumption on the process. Approximate confidence intervals for the intensity of the corresponding random measure are constructed in the case of fibre processes.
We prove a central limit theorem for linear triangular
arrays under weak dependence conditions. Our result is then applied
to dependent random variables sampled by a
-valued transient random walk. This extends the results
obtained by [N. Guillotin-Plantard and D. Schneider, Stoch. Dynamics3 (2003) 477–497]. An application
to parametric estimation by random sampling is also provided.
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