Universität zu Köln

Gorjao, Leonardo Rydin, Witthaut, Dirk ORCID: 0000-0002-3623-5341, Lehnertz, Klaus ORCID: 0000-0002-5529-8559 and Lind, Pedro G. (2021). Arbitrary-Order Finite-Time Corrections for the Kramers-Moyal Operator. Entropy, 23 (5). BASEL: MDPI. ISSN 1099-4300

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Gorjao, Leonardo Rydin UNSPECIFIED UNSPECIFIED UNSPECIFIED Witthaut, Dirk UNSPECIFIED orcid.org/0000-0002-3623-5341 UNSPECIFIED Lehnertz, Klaus UNSPECIFIED orcid.org/0000-0002-5529-8559 UNSPECIFIED Lind, Pedro G. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-590956
DOI:	10.3390/e23050517
Journal or Publication Title:	Entropy
Volume:	23
Number:	5
Date:	2021
Publisher:	MDPI
Place of Publication:	BASEL
ISSN:	1099-4300
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language DATA-DRIVEN RECONSTRUCTION; FOKKER-PLANCK EQUATION; DIFFUSION; PARAMETERS; EXPANSION; FIELD; DRIFT Multiple languages Physics, Multidisciplinary Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/59095