Journal of Statistical Physics, Vo/. 63, Nos. 1/2, 1991, p. 389-397.
A new perturbation method of finding the stationary distribution function of the form P=R*exp(-phi/D) for a metastable (anharmonic) system driven by exponentially correlated noise is presented. The noise term is modeled by a Langevin equation and the stationary solution of the resultant (2 + l)-dimensional Fokker-Planck equation is sought as a series expansion in the anharmonicity parameter around the known harmonic solution valid near the metastable minimum. The series converges for small t in the leading order of the noise intensity D anywhere within the well. Analytic expressions for phi and R were found for a metastable and a bistable potential. The resultant decay rate is in accordance with previously published results. The method is suitable also for numerical calculations.