Information Length Analysis of Linear Autonomous Stochastic Processes.

Abstract

When studying the behaviour of complex dynamical systems, a statistical formulation can provide useful insights. In particular, information geometry is a promising tool for this purpose. In this paper, we investigate the information length for n-dimensional linear autonomous stochastic processes, providing a basic theoretical framework that can be applied to a large set of problems in engineering and physics. A specific application is made to a harmonically bound particle system with the natural oscillation frequency , subject to a damping and a Gaussian white-noise. We explore how the information length depends on and , elucidating the role of critical damping in information geometry. Furthermore, in the long time limit, we show that the information length reflects the linear geometry associated with the Gaussian statistics in a linear stochastic process.