Parabolic Itô equations with monotone nonlinearities

In this paper the equation u_t = Lu ? F(u) + α(t, ω) is studied, where u(t) ?B₀ a Banach space. L is an unbounded self-adjoint negative definite operator. F is a monotone nonlinear potential operator. α(t, ω) is a white noise process on B₀. With suitable further restrictions on L and F it is proved that the equation has a unique solution. As t → ∞ the distribution of u(t, ω) approaches a stationary distribution which is calculated explicitly.