Characterization of stationary distributions using conditional expectations

We present a general formalism to characterize the probability density function of a set of dynamic variables in a stationary process using conditional expectations of kinematic observables on those variables. The formalism is exemplified with stochastic processes such as general Gaussian random processes and Brownian systems. We show that this formalism gives the Boltzmann distribution for equilibrium processes as it should and is applicable also for out of equilibrium processes. © 1999 Elsevier Science B.V. All rights reserved.