On the theory of KM2O-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 dissipation-dissipation theorem and a fluctuation-dissipation theorem, among the $K{M}_{2}O$-Langevin matrix associated with the pair of flows.