A new approach to a large class of stochastic differential equations (SDE) in Hilbert
spaces will be presented. It is based on a transformation turning the SDE into a
deterministic nonlinear equation on scaled L^p-spaces of random paths, which then
is proved to be solvable, employing techniques from nonlinear functional analysis.
This, in particular, applies to stochastic partial differential equations (SPDE),
including stochastic porous media equations, stochastic nonlinear parabolic
equations (as e.g. the stochastic Cauchy problem for the p-Laplacian) and stochastic
nonlinear transport equations. Apart from existence and uniqueness of solutions, this
way one also obtains new regularity results for solutions both in time and space.
Furthermore, in the “gradient case” as another consequence one gets a new
characterization of the solution to the SPDE, namely as the solution of a variational