Abstract
The theory of KM2O-Langevin equations for stochastic processes (or more generally, flows in inner product spaces) have been developed in view of applications to time series analysis (e.g., Okabe and Nakano, 1991; Okabe, 1999, 2000; Okabe and Matsuura, 2000). In Klimek et al. (2002) and Matsuura and Okabe (2001, 2003), we have investigated degenerate flows, which is important in the analysis of time series obtained from deterministic dynamical systems. As a continuation, we shall in this paper derive an efficient algorithm by which the minimum norm coefficients of KM2O-Langevin equations are explicitly obtained in degenerate cases. The obtained results have close relations to the calculations of conditional expectations such as nonlinear predictors of stochastic processes (Matsuura and Okabe, 2001). The method has also potential applications to financial mathematics.
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Matsuura, M. On a New Fluctuation–Dissipation Theorem for Degenerate Stationary Flows. Methodology and Computing in Applied Probability 5, 369–387 (2003). https://doi.org/10.1023/A:1026291304997
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DOI: https://doi.org/10.1023/A:1026291304997