On the theory of KM_2O-Langevin equations for stationary flows (1)

characterization theorem

Abstract

In this paper, we introduce a notion of stationarity for the pair of flows in a metric vector space and characterize it in such a way that there exist two relations, called a dissipatiov-dissipation theorem and a fluctuatiov-dissipation theorem, among the KM_2O-Langevin matrix associated with the pair of flows.