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| Hauptseite > Publikationsdatenbank > Arbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator > print |
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| 001 | 891975 | ||
| 005 | 20220930130314.0 | ||
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| 037 | _ | _ | |a FZJ-2021-01852 |
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| 100 | 1 | _ | |a Rydin Gorjão, Leonardo |0 P:(DE-Juel1)173608 |b 0 |e Corresponding author |
| 245 | _ | _ | |a Arbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator |
| 260 | _ | _ | |a Basel |c 2021 |b MDPI |
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| 520 | _ | _ | |a 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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| 700 | 1 | _ | |a Witthaut, Dirk |0 P:(DE-Juel1)162277 |b 1 |
| 700 | 1 | _ | |a Lehnertz, Klaus |0 0000-0002-5529-8559 |b 2 |
| 700 | 1 | _ | |a Lind, Pedro G. |0 0000-0002-8176-666X |b 3 |
| 773 | _ | _ | |a 10.3390/e23050517 |g Vol. 23, no. 5, p. 517 - |0 PERI:(DE-600)2014734-X |n 5 |p 517 - |t Entropy |v 23 |y 2021 |x 1099-4300 |
| 856 | 4 | _ | |u https://juser.fz-juelich.de/record/891975/files/Invoice_1177563.pdf |
| 856 | 4 | _ | |y OpenAccess |u https://juser.fz-juelich.de/record/891975/files/entropy-23-00517-v2.pdf |
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