Characterization of stationary distributions using conditional expectations

We present a general formalism to characterize the probability density func tion of a set of dynamic variables in a stationary process using conditiona l expectations of kinematic observables on those variables. The formalism i s exemplified with stochastic processes such as general Gaussian random pro cesses and Brownian systems. We show that this formalism gives the Boltzman n distribution for equilibrium processes as it should and is applicable als o for out of equilibrium processes. (C) 1999 Elsevier Science B.V. All righ ts reserved.