Inferring nonlinear fractional diffusion processes from single trajectories

Abstract

We present a method to infer the arbitrary space-dependent drift and diffusion of a nonlinear stochastic model driven by multiplicative fractional Gaussian noise from a single trajectory. Our method, fractional Onsager-Machlup optimisation (fOMo), introduces a maximum likelihood estimator by minimising a field-theoretic action which we construct from the observed time series. We successfully test fOMo for a wide range of Hurst exponents using artificial data with strong nonlinearities, and apply it to a data set of daily mean temperatures. We further highlight the significant systematic estimation errors when ignoring non-Markovianity, underlining the need for nonlinear fractional inference methods when studying real-world long-range (anti-)correlated systems.

21 pages, 5 figures, appendices

References in corpus (8)

• Anomalous transport in the crowded world of biological cells
• Measurement of Anomalous Diffusion Using Recurrent Neural Networks
• On the proper reconstruction of complex dynamical systems spoilt by strong measurement noise
• Rhythmicity, Recurrence, and Recovery of Flagellar Beating
• Stochastic actions for diffusive dynamics: Reweighting, sampling, and minimization
• Work distribution in time-dependent logarithmic-harmonic potential: exact results and asymptotic analysis
• Path probability ratios for Langevin dynamics -- exact and approximate
• Stochastic action for tubes: Connecting path probabilities to measurement