Chaos and nonlinear stochastic dynamics

This paper presents a discussion of certain aspects of the interrelationship between the chaotic response of some deterministic nonlinear dynamic system and the stochastic response of the corresponding system obtained by introducing a stochastic perturbation in the form of additive Gaussian white noise. The state space vector of the latter system can then often be represented as a Markov diffusion process. The joint probability density function of the state space vector of this Markov process is closely related to the corresponding chaotic attractor of the underlying deterministic system, and it will be demonstrated that it can be effectively used for prediction purposes.