Spatial Ergodicity for SPDEs

This lecture covers the concept of spatial ergodicity for Stochastic Partial Differential Equations (SPDEs), focusing on the behavior of solutions over time and space. The instructor discusses the basic problem formulation, conditions for spatial ergodicity, and the impact of initial data on the ergodic behavior. Various results related to ergodicity, weak mixing, and Central Limit Theorem in Total Variation are presented, along with the application of Malliavin Calculus and the Poincaré Inequality. The lecture concludes with a seminar overview on Stochastic Analysis, Random Fields, and Applications. Joint work with researchers from different universities is highlighted throughout the presentation.