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A stationary distribution for Langevin equations driven by colored noise is obtained, in the weak-noise limit, from the configuration-space Lagrangian-like function. The derivation makes no explicit use of Markovian, Fokker-Planck, or small-correlation-time approximations. Markovian approximations based on the Lagrangian, which do not involve truncated expansions, are also discussed.
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Colet et al. (1989) studied this question.
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