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Large deviations for the first exit time on small random perturbations of dynamical systems with a hyperbolic equilibrium point
We consider small random perturbations of dynamical systems \{X^{\epsilon}(t)\}_{0\leq t} (0<\epsilon) on a d-dimensional Euclidean space R^{d} when the origin 0\in R^{d} is a hyperbolic equilibrium point of unperturbed dynamical systems.The first exit time \tau_{D}^{\epsilon} of \{X^{\epsilon}(t)\}_{0\leq t} from a bounded domain D(\ni 0) of R^{d} obeys the large deviations …