Analyzing a stochastic process driven by Ornstein-Uhlenbeck noise

B. Lehle and J. Peinke
Phys. Rev. E 97, 012113 – Published 11 January 2018

Abstract

A scalar Langevin-type process X(t) that is driven by Ornstein-Uhlenbeck noise η(t) is non-Markovian. However, the joint dynamics of X and η is described by a Markov process in two dimensions. But even though there exists a variety of techniques for the analysis of Markov processes, it is still a challenge to estimate the process parameters solely based on a given time series of X. Such a partially observed 2D process could, e.g., be analyzed in a Bayesian framework using Markov chain Monte Carlo methods. Alternatively, an embedding strategy can be applied, where first the joint dynamics of X and its temporal derivative Ẋ is analyzed. Subsequently, the results can be used to determine the process parameters of X and η. In this paper, we propose a more direct approach that is purely based on the moments of the increments of X, which can be estimated for different time-increments τ from a given time series. From a stochastic Taylor expansion of X, analytic expressions for these moments can be derived, which can be used to estimate the process parameters by a regression strategy.

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  • Received 4 February 2017
  • Revised 14 December 2017

DOI:https://doi.org/10.1103/PhysRevE.97.012113

©2018 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Statistical Physics & Thermodynamics

Authors & Affiliations

B. Lehle and J. Peinke

  • Institute of Physics, University of Oldenburg, D-26111 Oldenburg, Germany

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Issue

Vol. 97, Iss. 1 — January 2018

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