Journal of Statistical Physics, Vol. 106, Nos. 1/2, January 2002, p. 57-96.
A trace formula is derived for the Fokker-Planck equation associated with Ito stochastic differential equations describing noisy time-continuous nonlinear dynamical systems. In the weak-noise limit, the trace formula provides estimations of the eigenvalues of the Fokker-Planck operator on the basis of the Pollicott-Ruelle resonances of the noiseless deterministic system, which is assumed to be non-bifurcating. At first order in the noise amplitude, the effect of noise on a periodic orbit is given in terms of the period and the derivative of the period with respect to the pseudo-energy of the Onsager-Machlup-Freidlin-Wentzell scheme.