DISTRIBUTION OF FLUCTUATIONAL PATHS IN NOISE-DRIVEN SYSTEMS

Dynamics of a system that performs a large fluctuation to a given stat e is essentially deterministic: the distribution of fluctuational path s peaks sharply at a certain optimal path along which the system is mo st likely to move. For the general case of a system driven by colored Gaussian noise, we provide a formulation of the variational problem fo r optimal paths. We also consider the prehistory problem, which makes it possible to analyze the shape of the distribution of fluctuational paths that arrive at a given state. We obtain, and solve in the limiti ng case, a set of linear equations for the characteristic width of thi s distribution. (C) 1998 Academic Press Limited.