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dc.contributor.authorGorjao, Leonardo
dc.contributor.authorWitthaut, Dirk
dc.contributor.authorLehnertz, Klaus
dc.contributor.authorLind, Pedro
dc.date.accessioned2022-08-11T11:49:09Z
dc.date.available2022-08-11T11:49:09Z
dc.date.created2021-12-12T19:45:06Z
dc.date.issued2021
dc.identifier.citationEntropy. 2021, 23 (5), 517en_US
dc.identifier.issn1099-4300
dc.identifier.urihttps://hdl.handle.net/11250/3011278
dc.description.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.en_US
dc.language.isoengen_US
dc.publisherMDPIen_US
dc.rightsNavngivelse 4.0 Internasjonal*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.no*
dc.titleArbitrary-order finite-Ttme corrections for the Kramers–Moyal operatoren_US
dc.typePeer revieweden_US
dc.typeJournal articleen_US
dc.description.versionpublishedVersionen_US
cristin.ispublishedtrue
cristin.fulltextoriginal
cristin.qualitycode1
dc.identifier.doi10.3390/e23050517
dc.identifier.cristin1967495
dc.source.journalEntropyen_US
dc.source.volume23en_US
dc.source.issue5en_US
dc.source.pagenumber517en_US


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