Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

Afin de comprendre les paramètres qui constituent l'équation de Frey et comment elle a été obtenue, on présentera le contexte financier.

A la suite de cette introduction, on cherchera les symétries de cette équation. Pour cela on expliquera la méthode d'Olver qui consiste à se placer dans un espace plus grand et à utiliser le prolongateur d'Olver puis on l'appliquera pas à pas à l'équation en question.

Nonlinear diffusion is an example of a gradient flow which arises as hydrodynamic limit of interacting particle systems. We will explain recent attempts to connect the macroscopic gradient flow structure, given by a  functional (entropy/free energy) and a metric, directly to a microscopic interacting particle system. (Joint work with P. Embacher, C. Reina, M. Stamatakis and J. Zimmer)

We consider the robust adaptive non parametric estimation problem for the periodic function observed in the continuous time regression model with the Lévy noises. We propose an adaptive model selection procedure, based on the improved weighted least square estimates.

We consider the problem of quick detection of abrupt parameter changes in an autoregressive model with Gaussian white noise. The time of change is deterministic but otherwise unknown. In contrast to detection algorithms for i.i.d.

We consider several models of diffusion processes with periodic in time trend coefficients and we describe the properties of the MLE and Bayes estimators of the frequency in the asymptotics of large samples and small noise. We start with the Signal in White Gaussian Noise model.

We consider a jump-type Cox–Ingersoll–Ross (CIR) process driven by a standard
Wiener process and a subordinator, and we study asymptotic properties of the maximum
likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical
and supercritical. In the subcritical case we prove weak consistency and asymptotic normality,
and, under an additional moment assumption, strong consistency as well. In the supercritical

This presentation addresses the problem of transient change detection. It is assumed that the duration of a transient change is usually short. In contrast to the conventional abrupt change detection, where the post-change period is assumed to be infinitely long, the detection of a transient change should be done before it disappears. The alert about the transient changes after their disappearance is considered as a missed detection.

We propose a sequential technique for the local polynomial estimation problem. We present our results in a context of data streams, for which we provide an asymptotic bias-variance decomposition of the considered estimator. Additionally, we study the asymptotic normality of the estimator and we provide algorithms for the practical use of the method in data streams framework.