Work

Inferring nonlinear fractional diffusion processes from single trajectories

Year: 2023

Type: article

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.

Source: New Journal of Physics

DOI: 10.1088/1367-2630/ad091e

Authors: Johannes A Kassel, Benjamin Walter, Holger Kantz

Institutions: Max Planck Institute for the Physics of Complex Systems, Imperial College London

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,365

Funders: Imperial College London, Ministero dell’Istruzione, dell’Università e della Ricerca