Date/heure
13 novembre 2025
10:45 - 11:45
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Randolf Altmeyer
Catégorie d'évènement Séminaire Probabilités et Statistique
Résumé
Stochastic partial differential equations (SPDEs) are a major subject of current research in probability and analysis, with rich methodologies for studying existence and regularity. At the same time, SPDEs are increasingly used as statistical models for spatially and temporally structured data, where inference requires learning unknown parameters or functions from observations. In this talk, we consider Bayesian inference for the reaction function in a stochastic reaction-diffusion equation, based on a single solution trajectory observed continuously in space over a fixed time interval. We place a Gaussian process prior on the reaction function and derive posterior contraction rates in a novel asymptotic regime in which the spatial domain grows while the observation horizon remains fixed. In this setting, the SPDE solution becomes spatially ergodic and converges to a stationary process, which allows us to prove concentration inequalities for spatial averages of the solution. The proofs combine tools from Malliavin calculus – most notably the Clark–Ocone formula – with sharp bounds on the marginal densities of the SPDE.