Chaos and randomness in dynamical systems

Abstract

In this paper, we discuss the irregularity found in the trajectories of "chaotic" differential equations from a new point of view--in terms of predictability of future values by optimal filters. This study, together with numerical results, indicates that as far as models for engineering phenomena are concerned, rather simple deterministic equations can be a completely satisfactory alternative to stochastic models in treating some aspects of estimation and stochastic control.