Inferring nonlinear fractional diffusion processes from single trajectories

Autor:	Kassel, Johannes A., Walter, Benjamin, Kantz, Holger
Rok vydání:	2023
Předmět:	Nonlinear Sciences - Adaptation and Self-Organizing Systems Condensed Matter - Statistical Mechanics Physics - Data Analysis Statistics and Probability
Druh dokumentu:	Working Paper
DOI:	10.1088/1367-2630/ad091e
Popis:	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. Comment: 21 pages, 5 figures, appendices
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2304.02536 Zobrazit plný text záznamu View this record from Arxiv