Bernard Bercu

Sharp large deviations for the fractional Ornstein-Uhlenbeck process (2008)

We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the...

Bercu, Bernard, Coutin, Laure, Savy, Nicolas

We investigate the sharp large deviation properties of the energy and the maximum likelihood estimator for the Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst index...

Almost Sure Stabilization for Adaptive Controls of Regime-switching LQ Systems with A Hidden Markov Chain (2008)

Bercu, Bernard, Dufour, Francois, Yin, G. George

This work is devoted to the almost sure stabilization of adaptive control systems that involve an unknown Markov chain. The control system displays continuous dynamics represented by differential...

Asymptotic analysis for bifurcating autoregressive processes via a martingale approach (2008)

Bercu, Bernard, De Saporta, Benoite, Gegout-Petit, Anne

We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process,...

A new concept of strong controllability via the Schur complement in adaptive tracking (2008)

Bercu, Bernard, Vazquez, Victor

We propose a new concept of strong controllability associated with the Schur complement of a suitable limiting matrix. This concept allows us to extend the previous results associated with...

Kernel density estimation and goodness-of-fit test in adaptive tracking (2008)

A moment approach for the almost sure central limit theorem for martingales (2008)

We investigate the asymptotic properties of a recursive kernel density estimator associated with the driven noise of a linear regression in adaptive tracking. We provide an almost sure pointwise and...

Exponential inequalities for self-normalized martingales with applications (2008)

We prove the almost sure central limit theorem for martingales via an original approach which uses the Carleman moment theorem together with the convergence of moments for powers of martingales....

Bercu, Bernard, Touati, Abderrahmen

We propose several exponential inequalities for self-normalized martingales similar to those established by De la Pena. The keystone is the introduction of a new notion of random variable heavy on...

Fluctuations of Interacting Markov Chain Monte Carlo Models (2008)

A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models (2008)

We present a functional central limit theorem for a general class of interacting Markov chain Monte Carlo interpretations of discrete generation measure-valued equations. The path space models...

Fluctuations of Interacting Markov Chain Monte Carlo Models (2008)

We present a functional central limit theorem for a new class of interaction Markov chain Monte Carlo interpretations of discrete generation measure valued equations. We provide an original...

A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models (2008)

We present a functional central limit theorem for a general class of interacting Markov chain Monte Carlo interpretations of discrete generation measure-valued equations. The path space models...

Exponential inequalities for self-normalized martingales with applications (2008)

We present a functional central limit theorem for a new class of interaction Markov chain Monte Carlo interpretations of discrete generation measure valued equations. We provide an original...

Bercu, Bernard, Touati, Abderrahmen

We propose several exponential inequalities for self-normalized martingales similar to those established by De la Pena. The keystone is the introduction of a new notion of random variable heavy on...

Kernel density estimation and goodness-of-fit test in adaptive tracking (2008)

A moment approach for the almost sure central limit theorem for martingales (2008)

We investigate the asymptotic properties of a recursive kernel density estimator associated with the driven noise of a linear regression in adaptive tracking. We provide an almost sure pointwise and...

On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications (2008)

We prove the almost sure central limit theorem for martingales via an original approach which uses the Carleman moment theorem together with the convergence of moments for powers of martingales....

On the Almost Sure Central Limit Theorem for Vector Martingales: Convergence of Moments and Statistical Applications (2008)

We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the...

A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models (2008)

We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the...

A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models (2008)

We present a functional central limit theorem for a new class of interaction Markov chain Monte Carlo interpretations of discrete generation measure valued equations. We provide an original...

Spectrum of the product of Toeplitz matrices with application in probability (2007)

We present a functional central limit theorem for a new class of interaction Markov chain Monte Carlo interpretations of discrete generation measure valued equations. We provide an original...

Bercu, Bernard, Bony, Jean-Francois, Bruneau, Vincent

We study the spectrum of the product of two Toeplitz operators. Assume that the symbols of these operators are continuous and real-valued and that one of them is non-negative. We prove that the...

Exponential inequalities for self-normalized martingales with applications (2007)

Bercu, Bernard, Touati, Abderrahmen

We propose several exponential inequalities for self-normalized martingales similar to those established by De la Pe\~{n}a. The keystone is the introduction of a new notion of random variable heavy...

Asymptotic results for empirical measures of weighted sums of independent random variables (2007)

Bercu, Bernard; Universite Bordeaux 1; Bernard.Bercu@math.u-bordeaux1.fr, Bryc, Wlodek; University Of Cincinnati; Brycw@math.uc.edu

We investigate the asymptotic behavior of weighted sums of independent standardized random variables with uniformly bounded third moments. The sequence of weights is given by a family of rectangular...

Asymptotic results for empirical measures of weighted sums of independent random variables (2007)

Bercu, Bernard; Universite Bordeaux 1; Bernard.Bercu@math.u-bordeaux1.fr, Bryc, Wlodek; University Of Cincinnati; Brycw@math.uc.edu

We investigate the asymptotic behavior of weighted sums of independent standardized random variables with uniformly bounded third moments. The sequence of weights is given by a family of rectangular...

Asymptotic results for empirical measures of weighted sums of independent random variables (2006)

Bercu, Bernard, Bryc, Wlodzimierz

We prove that if a rectangular matrix with uniformly small entries and approximately orthogonal rows is applied to the independent standardized random variables with uniformly bounded third moments,...

We investigate the spectral asymptotic properties of the stationary dynamical system $\xi_t=\varphi(T^t(X_0))$. This process is given by the iterations of a piecewise expanding map $T$ of the...

We investigate the spectral asymptotic properties of the stationary dynamical system $\xi_t=\varphi(T^t(X_0))$. This process is given by the iterations of a piecewise expanding map $T$ of the...

Convergence des moments dans le théorème de la limite centrale presque sûr pour les martingales vectorielles (2006)

We investigate the spectral asymptotic properties of the stationary dynamical system $\xi_t=\varphi(T^t(X_0))$. This process is given by the iterations of a piecewise expanding map $T$ of the...

Convergence des moments dans le théorème de la limite centrale presque sûr pour les martingales vectorielles (2006)

In this report, new almost sure convergence properties for vectorial martingale transforms are established. Assuming some regularity conditions both on the increasing process and on the moments of...

Convergence des moments dans le théorème de la limite centrale presque sûr pour les martingales vectorielles (2006)

In this report, new almost sure convergence properties for vectorial martingale transforms are established. Assuming some regularity conditions both on the increasing process and on the moments of...

In this report, new almost sure convergence properties for vectorial martingale transforms are established. Assuming some regularity conditions both on the increasing process and on the moments of...

Kernel density estimation and goodness-of-fit test in adaptive tracking (2005)

We investigate the spectral asymptotic properties of the stationary dynamical system $\xi_t=\varphi(T^t(X_0))$. This process is given by the iterations of a piecewise expanding map $T$ of the...

On Carleman approach for the almost sure central limit theorem for martingales (2005)

We investigate the asymptotic properties of a recursive kernel density estimator associated with the driven noise of a linear regression in adaptive tracking. We provide an almost sure pointwise and...

Kernel density estimation and goodness-of-fit test in adaptive tracking (2005)

We prove the almost sure central limit theorem for martingales via an original approach which uses the Carleman moment theorem together with the convergence of moments for powers of martingales....

On Carleman approach for the almost sure central limit theorem for martingales (2005)

We investigate the asymptotic properties of a recursive kernel density estimator associated with the driven noise of a linear regression in adaptive tracking. We provide an almost sure pointwise and...