Stochastic evolution equations with rough boundary noise

Abstract

AbstractWe investigate the pathwise well-posedness of stochastic partial differential equations perturbed by multiplicative Neumann boundary noise, such as fractional Brownian motion for $$H\in (1/3,1/2].$$ H ∈ ( 1 / 3 , 1 / 2 ] . Combining functional analytic tools with the controlled rough path approach, we establish global existence of solutions and flows for such equations. For Dirichlet boundary noise we obtain similar results for smoother noise, i.e. in the Young regime.