dc.contributor.author | Gorjao, Leonardo | |
dc.contributor.author | Witthaut, Dirk | |
dc.contributor.author | Lehnertz, Klaus | |
dc.contributor.author | Lind, Pedro | |
dc.date.accessioned | 2022-08-11T11:49:09Z | |
dc.date.available | 2022-08-11T11:49:09Z | |
dc.date.created | 2021-12-12T19:45:06Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Entropy. 2021, 23 (5), 517 | en_US |
dc.identifier.issn | 1099-4300 | |
dc.identifier.uri | https://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.iso | eng | en_US |
dc.publisher | MDPI | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Arbitrary-order finite-Ttme corrections for the Kramers–Moyal operator | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | publishedVersion | en_US |
cristin.ispublished | true | |
cristin.fulltext | original | |
cristin.qualitycode | 1 | |
dc.identifier.doi | 10.3390/e23050517 | |
dc.identifier.cristin | 1967495 | |
dc.source.journal | Entropy | en_US |
dc.source.volume | 23 | en_US |
dc.source.issue | 5 | en_US |
dc.source.pagenumber | 517 | en_US |