Langevin equations from time series

9 February 2005

journal article
research article
Published by American Physical Society (APS) in Physical Review E

Vol. 71 (2) , 027101
https://doi.org/10.1103/physreve.71.027101

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.

Keywords

This publication has 20 references indexed in Scilit:

Analysis of time series from stochastic processes
Physical Review E, 2000
Extracting model equations from experimental data
Physics Letters A, 2000
How to Quantify Deterministic and Random Influences on the Statistics of the Foreign Exchange Market
Physical Review Letters, 2000
Generation of compound non-Gaussian random processes with a given correlation function
Physical Review E, 2000
Analysis of data sets of stochastic systems
Physics Letters A, 1998
On the generation of the baseband and narrowband non-Gaussian processes
IEEE Transactions on Signal Processing, 1998
Statistical properties of a turbulent cascade
Physica D: Nonlinear Phenomena, 1997
Description of a Turbulent Cascade by a Fokker-Planck Equation
Physical Review Letters, 1997
Stochastic differential equations: an approach to the generation of continuous non-Gaussian processes
IEEE Transactions on Signal Processing, 1995
Stationary probability density functions: An exact result
Physics of Fluids A: Fluid Dynamics, 1993