Asymptotic couplings by reflection and applications for nonlinear monotone SPDES

作者：Wang, Feng-Yu^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2015, 117: 169-188.

DOI：10.1016/j.na.2015.01.012

• Gradient estimate
• Holder continuity
• Exponential convergence
• Asymptotic couplings by reflection
• Stochastic partial differential equation

Asymptotic couplings by reflection are constructed for a class of nonlinear monotone SPDEs (stochastic partial differential equations). As applications, gradient/Holder 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 p-Laplacian equations, and stochastic generalized fast-diffusion equations. We emphasize that the gradient estimate is studied for the first time for these equations.

• 出版日期2015-4
• 单位北京师范大学