Estimation of drift and diffusion functions from time series data: A maximum likelihood framework

Abstract

Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic dynamics in time. Recently techniques for the estimation of the corresponding stochastic differential equations from measured data have been introduced. This contribution develops a framework for the estimation of the functions and their respective (Bayesian posterior) confidence regions based on likelihood estimators. In succession approximations are introduced that significantly improve the efficiency of the estimation procedure. While being consistent with standard approaches to the problem this contribution solves important problems concerning the applicability and the accuracy of estimated parameters.

18 pages, 2 figures

References in corpus (7)

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• Finite sampling interval effects in Kramers-Moyal analysis
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• Extracting strong measurement noise from stochastic series: applications to empirical data
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• Maximum likelihood estimates of diffusion coefficients from single-particle tracking experiments
• Extended Kramers-Moyal analysis applied to optical trapping
• Master equation for She-Leveque scaling and its classification in terms of other Markov models of developed turbulence
• Quantifying resilience and the risk of regime shifts under strong correlated noise
• Inferring nonlinear fractional diffusion processes from single trajectories
• Assessing the Suitability of the Langevin Equation for Analyzing Measured Data Through Downsampling