Date/heure
7 décembre 2023
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Xue-Mei Li (Imperial College London & EPFL)
Catégorie d'évènement Séminaire Probabilités et Statistique
Résumé
It is a standard assumption that the Gaussian noises in stochastic systems are white in time and white space. This means that the noise at different point in space or in time are assumed to be uncorrelated. This leads to the Ito theory of integration. However, some time series data and other data indicate otherwise, some even exhibits long range dependence. In SDEs these imply that neither the Markov theory nor its martingale characterisation can be relied on. In SPDEs, the difficulty of irregularity coming from the white noise can be mitigated if they are replaced by smooth correlated noise. But other problems arrive. In this talk we shall explore these models and some phenomenons. New, as well as old, techniques in Stochastic Analysis will be explored.