Langevin equations from time series

E. Racca and A. Porporato
Phys. Rev. E 71, 027101 – Published 9 February 2005

Abstract

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.

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  • Received 18 August 2004

DOI:https://doi.org/10.1103/PhysRevE.71.027101

©2005 American Physical Society

Authors & Affiliations

E. Racca

  • Dipartimento di Idraulica, Trasporti e Infrastrutture Civili, Politecnico di Torino, Torino, Italy

A. Porporato*

  • Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina 27708, USA

  • *Electronic address: amilcare@duke.edu

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Vol. 71, Iss. 2 — February 2005

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