Rescaling nonlinear noise for 1D stochastic parabolic equations

Beniamin Goldys, Misha Neklyudov

Abstract

We show regularisation effect of nonlinear gradient noise to the solution ofn1D stochastic parabolic equation. We demonstrate convergence to a martingale (independent upon space variable) when we rescale the noise at the extremum points of the process.

Keywords: regularization by noise, regularity, stochastic PDE.

AMS Subject Classification: Primary 60H15; secondary 37K99.