Dynamical systems perturbed by small random noise have received a vast attention
over the last decades in many areas of science extending from physics through
chemistry and biology to climatology. They typically represent a deterministic
large scale phenomenon expressed in terms of an ordinary or partial differential
equation which inherits the noisy residual of a rapidly fluctuating low intensity
perturbation on much smaller scales. Commonly, these systems largely mimic the
phenomenon’s unperturbed deterministic behavior up to a characteristic time scale.
This scale is a function of the intensity of the perturbation, depends essentially on
the underlying nature of the noise and, to a minor extent, on the state space geometry
of the deterministic system. Beyond that scale the system exhibits noise induced
excursions.