A short introduction to Stochastic PDEs

Charles-Edouard Bréhier (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHERIALS - MATHematics for MatERIALS

The main two aims of these lecture notes are: a definition of the space-time white noise and the study of second-order stochastic evolution equations of parabolic type. The main points are the regularity properties, in time and in space, of the solutions. A few results on the numerical approximation are also given at the end. The content is based on the lectures delivered at CERMICS in March 2014.

Domaines: Probabilités [math.PR]; Analyse numérique [math.NA]

Charles-Edouard Bréhier. A short introduction to Stochastic PDEs. 2014. ⟨hal-00973887v2⟩