Langevin equations from time series.
We discuss the link between the approach to obtain the drift and diffusion of one-dimensional Langevin equations from time series, and Pope and Ching's relationship for stationary signals. The two approaches are based on different interpretations of conditional averages of the time derivatives of the time series at given levels. The analysis provides a useful indication for the correct application of Pope and Ching's relationship to obtain stochastic differential equations from time series and shows its validity, in a generalized sense, for nondifferentiable processes originating from Langevin equations.
Racca
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Dipartimento di Idraulica, Trasporti e Infrastrutture Civili, Politecnico di Torino, Torino, Italy.
Porporato
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