Hierarchical aggregation of diffusion processes with multiple equilibrium points

When a dynamical system with multiple equilibrium points is perturbed by continous wide-band noise, it is known that transitions between different equilibrium points occur with probability one. An important problem associated with the analysis of these systems is the statistical characterization of the jump process which represents the transitions between different domains of attraction. A physical example of a dynamical system with multiple equilibrium point are common is an interconnected power system, where the swing equations [1] represent a system with many possible equilibrium angles, defined by a power balance between electrical supply and demand. When the demand fluctuations and unmodeled effects are represented as additive random noise, the resulting system undergoes transitions between the equilibrium points.