Analysis of time series from stochastic processes

@article{Gradisek2000AnalysisOT,
  title={Analysis of time series from stochastic processes},
  author={Gradisek and Siegert and Friedrich and Grabec},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  year={2000},
  volume={62 3 Pt A},
  pages={
          3146-55
        }
}
  • Gradisek, Siegert, +1 author Grabec
  • Published 1 September 2000
  • Mathematics
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
Analysis of time series from stochastic processes governed by a Langevin equation is discussed. Several applications for the analysis are proposed based on estimates of drift and diffusion coefficients of the Fokker-Planck equation. The coefficients are estimated directly from a time series. The applications are illustrated by examples employing various synthetic time series and experimental time series from metal cutting. 
Examples of Analysis of Stochastic Processes Based on Time Series Data
Time series data from stochastic processes described by the Langevin equation are analyzed. Analysis is based on estimation of the deterministic and random terms of the Langevin equation from data.
Langevin equations from time series.
  • E. Racca, A. Porporato
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    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
TLDR
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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In this article we discuss an extension of a method to extract Langevin equations from noisy time series to spatio-temporal data governed by stochastic partial differential equations (SPDEs). The
Stochastic Time Series with Strong, Correlated Measurement Noise: Markov Analysis in N Dimensions
An extension and generalization of a recently presented approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For a stochastic
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The proposed data-analysis method yields dynamical models in terms of stochastic delay differential equations on the basis of which differential effects of driving forces and time-delayed feedback forces can be identified.
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Concepts for the analysis of observed scalar time series data in reconstructed vector valued phase spaces are reviewed. Originally exclusively designed for data from deterministic chaotic systems,
Reconstruction of stochastic nonlinear dynamical models from trajectory measurements.
TLDR
An algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data that does not require an extensive global search for the model parameters, provides optimal compensation for the effects of dynamical noise, and is robust for a broad range of dynamicals models.
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