Asymptotic couplings by reflection and applications for nonlinear monotone SPDES

Asymptotic couplings by reflection are constructed for a class of nonlinear monotone SPDEs (stochastic partial differential equations). As applications, gradient/Hölder estimates as well as exponential convergence are derived for the associated Markov semigroup. The main results are illustrated by stochastic generalized porous media equations, stochastic pp-Laplacian equations, and stochastic generalized fast-diffusion equations. We emphasize that the gradient estimate is studied for the first time for these equations.