ABSTRACT. In this paper it is shown how Jaynes' maximum entropy principle or, more generally, his maximum calibre principle can be cast in such a form that the stochastic process that underlies observed data can be determined under the assumption that the process is Markovian. Under suitable constraints it becomes possible to derive the Fokker-Planck equation and the Îto-Langevin equation of that process.

Introduction

Jaynes' maximum entropy principle has found wide-spread applications not only in systems in thermoequilibrium but also in systems far from it. In addition, Jaynes treated time-dependent processes by means of his maximum calibre principle. In the present paper we show how his principles can be cast in such a form that the underlying process that is observed by certain correlation functions can be represented by a Fokker-Planck equation and an Îto-Langevin equation. It will be assumed throughout our paper that the process is Markovian. At the end of this contribution explicit examples treated recently by Lisa Borland and the present author will be presented.

Derivation of the Fokker-Planck Equation

In order to express the definition of a Markov process in a rigorous mathematical form, we choose a time sequence t0, t1, …tM. We may attribute a probability distribution to the path taken by the state vectors at the corresponding times.