Journal Article

FZJ-2021-01852

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Arbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator

Rydin Gorjão, L. (Corresponding author)FZJ* ; Witthaut, D.FZJ* ; Lehnertz, K. ; Lind, P. G.

2021
MDPI Basel

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Please use a persistent id in citations: http://hdl.handle.net/2128/27686  doi:10.3390/e23050517

Abstract: With the aim of improving the reconstruction of stochastic evolution equations from empirical time-series data, we derive a full representation of the generator of the Kramers–Moyal operator via a power-series expansion of the exponential operator. This expansion is necessary for deriving the different terms in a stochastic differential equation. With the full representation of this operator, we are able to separate finite-time corrections of the power-series expansion of arbitrary order into terms with and without derivatives of the Kramers–Moyal coefficients. We arrive at a closed-form solution expressed through conditional moments, which can be extracted directly from time-series data with a finite sampling intervals. We provide all finite-time correction terms for parametric and non-parametric estimation of the Kramers–Moyal coefficients for discontinuous processes which can be easily implemented—employing Bell polynomials—in time-series analyses of stochastic processes. With exemplary cases of insufficiently sampled diffusion and jump-diffusion processes, we demonstrate the advantages of our arbitrary-order finite-time corrections and their impact in distinguishing diffusion and jump-diffusion processes strictly from time-series data.

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Contributing Institute(s):

1. Systemforschung und Technologische Entwicklung (IEK-STE)

Research Program(s):

1. 111 - Energiesystemtransformation (POF4-111) (POF4-111)

Appears in the scientific report 2021

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