Klimek, Maciej; Karlsson, Erlendur; Matsuura, Masaya; Okabe, Yasunori A geometric proof of the fluctuation-dissipation theorem for the KM\(_2\)O-Langevin equation. (English) Zbl 1009.60029 Hokkaido Math. J. 31, No. 3, 615-628 (2002). Summary: We give a short proof, based on the geometry of inner product spaces, of the fluctuation-dissipation theorem that asserts applicability of the Whittle-Wiggins-Robinson algorithm in the context of the \(\text{KM}_2\text{O}\)-Langevin equations also in degenerate and non-stationary cases. Cited in 1 ReviewCited in 2 Documents MSC: 60G25 Prediction theory (aspects of stochastic processes) 60G12 General second-order stochastic processes 82C05 Classical dynamic and nonequilibrium statistical mechanics (general) Keywords:non-stationarity property; degeneracy property; update property; fluctuation-dissipation theorem; \(\text{KM}_2\text{O}\)-Langevin equation PDFBibTeX XMLCite \textit{M. Klimek} et al., Hokkaido Math. J. 31, No. 3, 615--628 (2002; Zbl 1009.60029) Full Text: DOI