Simulation of Rare Events in Stochastic Systems

Abstract

Abstract The paper presents algorithms for simulation rare events in stochastic systems based on the theory of large deviations. Here, this approach is used in conjunction with the tools of optimal control theory to estimate the probability that some observed states in a stochastic system will exceed a given threshold by some upcoming time instant. Algorithms for obtaining controlled extremal trajectory (A-profile) of the system, along which the transition to a rare event (threshold) occurs most likely under the influence of disturbances that minimize the action functional, are presented. It is also shown how this minimization can be efficiently performed using numerical-analytical methods of optimal control for linear and nonlinear systems. These results are illustrated by an example for a precipitation-measured monsoon intraseasonal oscillation (MISO) described by a low-order nonlinear stochastic model.