Equivalent random force and time-series model in systems far from equilibrium

Abstract

Under the condition that observed time-series data is given, a stochastic Markovian equation for a physical system can be transformed into an observable non-Markovian equation used in the time-series analysis. The physical random force satisfying the fluctuation dissipation theorem is also transformed into a stochastically equivalent random force in the derivation of the time-series model of observable variables. Statistical quantities, i.e., correlation and power spectral density functions for observable variables, can be expressed not only by the physical random force, but also by the equivalent random force. A relation between the variance of physical random force and that of equivalent random force is also found.