Stochastic two-scale convergence in the mean and applications.
Stochastic weak attractor for a dissipative Euler equation.
Strong Feller solutions to SPDE's are strong Feller in the weak topology
For a wide class of Markov processes on a Hilbert space H, defined by semilinear stochastic partial differential equations, we show that their transition semigroups map bounded Borel functions to functions weakly continuous on bounded sets, provided they map bounded Borel functions into functions continuous in the norm topology. In particular, an Ornstein-Uhlenbeck process in H is strong Feller in the norm topology if and only if it is strong Feller in the bounded weak topology. As a consequence,...
Symmetrized solutions for nonlinear stochastic differential equations.