https://doi.org/10.1140/epjb/s10051-025-00883-9
Regular Article - Statistical and Nonlinear Physics
Local statistical moments to capture Kramers–Moyal coefficients
1
School of Mathematics and Science, Institute of Physics, Carl von Ossietzky Universität Oldenburg, 26129, Oldenburg, Germany
2
ForWind, Center for Wind Energy Research, Küpkersweg 70, 26129, Oldenburg, Germany
3
ICBM, Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky Universität Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26129, Oldenburg, Germany
a
christian.wiedemann@uni-oldenburg.de
Received:
2
May
2024
Accepted:
10
February
2025
Published online:
20
February
2025
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.
© The Author(s) 2025
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