Local statistical moments to capture Kramers–Moyal coefficients

Christian Wiedemann (), Matthias Wächter, Jan A. Freund and Joachim Peinke
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Christian Wiedemann: Carl von Ossietzky Universität Oldenburg
Matthias Wächter: Carl von Ossietzky Universität Oldenburg
Jan A. Freund: Carl von Ossietzky Universität Oldenburg
Joachim Peinke: Carl von Ossietzky Universität Oldenburg

The European Physical Journal B: Condensed Matter and Complex Systems, 2025, vol. 98, issue 2, 1-13

Abstract: Abstract This study introduces an innovative local statistical moment approach for estimating Kramers–Moyal coefficients, effectively bridging the gap between nonparametric and parametric methodologies. These coefficients play a crucial role in characterizing stochastic processes. Our proposed approach provides a versatile framework for localized coefficient estimation, combining the flexibility of nonparametric methods with the interpretability of global parametric approaches. We showcase the efficacy of our approach through use cases involving both stationary and non-stationary time series analysis. Additionally, we demonstrate its applicability to real-world complex systems, specifically in the energy conversion process analysis of a wind turbine. Graphic abstract

Date: 2025
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DOI: 10.1140/epjb/s10051-025-00883-9

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