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arXiv · 2304.02536

Inferring nonlinear fractional diffusion processes from single trajectories

Johannes A. Kassel·Benjamin Walter·Holger Kantz
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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.

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Johannes A. Kassel, Benjamin Walter, Holger Kantz. 2023-04-05. Inferring nonlinear fractional diffusion processes from single trajectories. https://doi.org/10.1088/1367-2630/ad091e

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