Séminaire Franco-Cubain de mathématiques (vendredi 14 juin)

7 juin 24

Le prochain séminaire Franco-Cubain de mathématiques se réunira le vendredi 14 juin à 15h à Sorbonne Université, en salle 1516-3-09 LJLL, couloir 15-16, salle 309 (voici le plan d’accès).

Nous aurons le plaisir d’écouter nos collègues, 

  • Claudia Fonte Sánchez, Inria Grenoble

Existence and stability in the voltage-conductance equation

This talk delves into the non-linear kinetic Voltage-Conductance equation, a crucial mathematical model for understanding neuronal activity. We obtain two key results in a framework suitable for weak interactions. First, we establish the existence of solutions. Second, we prove linear asymptotic exponential stability of the steady state. This stability result builds upon a recent estimate by Dou (2023) and offers a constructive approach. Both results are based in a fundamental way on some ultracontractivity property of the flow associated to the linear of the Voltage-Conductance equation. 

  • Carlos Fernández, Institut Polytechnique de Paris

Harris recurrent Markov chains and nonlinear monotone cointegrated models

In this presentation, we study a nonlinear cointegration-type model of the form \(Z_t = f_0(X_t) + W_t\) where \(f_0\) is a monotone function and \(X_t\) is a Harris recurrent Markov chain. We use a nonparametric Least Square Estimator to locally estimate \(f_0\), and under mild conditions, we show its strong consistency and obtain its rate of convergence. New results (of the Glivenko-Cantelli type) for localized null recurrent Markov chains are also presented.

Si vous souhaitez participer à distance, voici le lien de la séance : https://orsay.bbb.cnrs.fr/b/cor-sro-cqc-yyr.