Asymptotic analysis of nonlinear systems with small stochastic perturbations

By stochastic perturbations of white noise type, a nonlinear system will with probability 1 leave any bounded domain of state space that contains a stable equilibrium of the system. The escape time and its statistics are a measure for the stochastic stability of the system. Its statistical moments are found from the asymptotic solution of the singularly perturbed Fokker—Planck equation. For higher-dimensional systems, a numerical method has been developed for computing certain constants in the asymptotic solution of this equation. The method is applied to mechanical systems with stochastic input, stochastic population problems and to dynamical systems with multiple stable equilibria arising in hydrodynamics.