Exponential Ergodicity and Raleigh-schrödinger Series for Infinite Dimensional Diffusions
نویسنده
چکیده
, with η ∈ T d , where the coefficients ai, bi are finite range, bounded with bounded second order partial derivatives and the ellipticity assumption infi,η ai(η) > 0 is satisfied. We prove that whenever ν is an invariant measure for this diffusion satisfying the logarithmic Sobolev inequality, then the dynamics is exponentially ergodic in the uniform norm, and hence ν is the unique invariant measure. As an application of this result, we prove that if A = P
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