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The aim of this paper is to study the convergence of the solution of theFokker-Planck equation to the associated stationary state when time goes toinfinity. The force field which we consider here is of a general structure,that is it may not derive from a potential. The proof is based on an adequatesplitting L = B+A of the Fokker-Planck operator L and the use of Krein-Rutmanntheory.

Convergence to equilibrium for Fokker-Planck equation with a general force field