(1) Technische Universität Berlin, FB 3, MA 7-5, TU Berlin, Straße des 17. Juni 136, D-10623 Berlin, Germany
Abstract:
We study a new kind of backward doubly stochastic differential equations, where the nonlinear noise term is given by Itô–Kunita's stochastic integral. This allows us to give a probabilistic interpretation of classical and Sobolev's solutions of semilinear parabolic stochastic partial differential equations driven by a nonlinear space-time noise.