A regularity theorem for quasilinear parabolic systems under random perturbations

Several aspects of regularity theory for parabolic systems are investigated under the effect of random perturbations. The deterministic theory, when strict parabolicity is assumed, presents both classes of systems where all weak solutions are in fact more regular, and examples of systems with weak solutions which develop singularities in finite time. Our main result is the extension of a regularity result due to Kalita to the stochastic case, which concerns local Holder continuity of weak solutions in the vectorial case. For the proof, we apply stochastic versions of methods, which are classical in the deterministic case (such as difference quotient techniques, higher integrability by embedding theorems, and a version of Moser's iteration technique). This might be of interest on their own.