Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

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In this talk, I will present an overview of recent results on finite-sample Probably Approximately Correct (PAC) and PAC-Bayesian bounds for learning partially observed dynamical systems in state-space form. For clarity, we begin with linear stochastic systems in discrete time, learned from a single trajectory, and then discuss extensions to more complex nonlinear settings.

The emergence of mean-curvature flow of an interface between different phases or populations is a phenomenon of long standing interest in statistical physics.  
In this talk, we review recent progress with respect to a class of reaction-diffusion stochastic particle systems on an $n$-dimensional lattice.
In such a process, particles can move across sites as well as be created/annihilated according to diffusion and reaction rates.  
These rates will be chosen so that there are two preferred particle mass density levels $a_1$, $a_2$ in `balance'.

Building on the presentation given at the colloquium on September 11, we go into some of the details of the homogenizations needed to obtain the sharp interface limit and associated fluctuations.

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We study estimation and inference for the mean of real-valued random func- tions defined on a hypercube. The independent random functions are observed on a discrete, random subset of design points, possibly with heteroscedastic noise. We propose a novel optimal-rate estimator based on Fourier series expansions and establish a sharp non-asymptotic error bound in L2−norm.

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Peer-to-peer (P2P) insurance promises lower costs and better alignment of interests by having small groups of policyholders directly share risk. Yet full pooling can destroy prevention incentives under moral hazard, while self-insurance sacrifices diversification. In this talk, we develop a unified mean–variance framework that endogenizes both the pooling matrix and the effort levels in one joint optimization.