• Lecturer: Benjamin Gess
• Date: Monday 16:15 - 17:45
• Room: MPI MiS, A3 01
• Language: English
• Target audience: MSc students, PhD students, Postdocs
• Prerequisites: functional analysis, basic convex analysis

Abstract

In this lecture series we will introduce the concept of stochastic variational inequalities (SVI) as a concept of solutions to SPDE. Our interest in this concept of solutions comes from two directions: First, SVI solutions can be used in certain situations in which the "variational" approach to SPDE fails, e.g. for multi-valued SPDE. We will encounter this in the application to the stochastic total variation flow, with links to self-organized criticality. Second, the concept of SVI solutions offers nice stability properties with respect to perturbations, which will be demonstrated by introducing a stochastic analog of Mosco-convergence. This yields a sufficient condition for the convergence of the corresponding solutions to SPDE. The general theory will be laid out by proving the convergence of non-local approximations to local stochastic p-Laplace equations.