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April, 2003 On the theory of KM2O-Langevin equations for non-stationary and degenerate flows
Masaya MATSUURA, Yasunori OKABE
J. Math. Soc. Japan 55(2): 523-563 (April, 2003). DOI: 10.2969/jmsj/1191419129


We have developed the theory of KM2O-Langevin equations for stationary and non-degenerate flow in an inner product space. As its generalization and refinement of the results in [14], [15], [16], we shall treat in this paper a general flow in an inner product space without both the stationarity property and the non-degeneracy property. At first, we shall derive the KM2O-Langevin equation describing the time evolution of the flow and prove the fluctuation-dissipation theorem which states that there exists a relation between the fluctuation part and the dissipation part of the above KM2O- Langevin equation. Next we shall prove the characterization theorem of stationarity property, the construction theorem of a flow with any given nonnegative definite matrix function as its two-point covariance matrix function and the extension theorem of a stationary flow without losing stationarity property.


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Masaya MATSUURA. Yasunori OKABE. "On the theory of KM2O-Langevin equations for non-stationary and degenerate flows." J. Math. Soc. Japan 55 (2) 523 - 563, April, 2003.


Published: April, 2003
First available in Project Euclid: 3 October 2007

zbMATH: 1162.82312
MathSciNet: MR1961299
Digital Object Identifier: 10.2969/jmsj/1191419129

Primary: 60G25
Secondary: 60G12 , 82C05

Keywords: $\mathrm{K}\mathrm{M}_{2}\mathrm{O}$-Langevin equation , degeneracy property , flow , fluctuation-dissipation theorem , non-stationarity property

Rights: Copyright © 2003 Mathematical Society of Japan


Vol.55 • No. 2 • April, 2003
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