Solutions of SPDE as zeros of maps on scaled path spaces
Date/Time:28 Aug 2019 14:00Venue: S17 #04-04 SR3Speaker: Michael Rockner, Bielefeld UniversitySolutions of SPDE as zeros of maps on scaled path spacesIt has been recently shown that the solutions of a large class of stochastic partial differential equations (SPDE) can be obtained as zeros of properly defined map on a path space equipped with a norm which is “scaled” by the exponential of a function-valued Brownian motion. In the talk this result will be reviewed and connected to current developments about the case where the underlying SPDE is a gradient flow, perturbed by linear multiplicative noise. In this case it follows from the above result and by applying methods from the calculus of variations that the solution minimizes a certain explicit convex functional on the path space. Applications include stochastic porous media equations, stochastic nonlinear parabolic equations (as e.g. the stochastic Cauchy problem for the p-Laplacian)and in the non-gradient case also stochastic nonlinear transport equations.Add to calendar:
