This title appears in the Scientific Report :
2021
Please use the identifier:
http://hdl.handle.net/2128/27686 in citations.
Please use the identifier: http://dx.doi.org/10.3390/e23050517 in citations.
Arbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator
Arbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator
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 differ...
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Personal Name(s): | Rydin Gorjão, Leonardo (Corresponding author) |
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Witthaut, Dirk / Lehnertz, Klaus / Lind, Pedro G. | |
Contributing Institute: |
Systemforschung und Technologische Entwicklung; IEK-STE |
Published in: | Entropy, 23 (2021) 5, S. 517 - |
Imprint: |
Basel
MDPI
2021
|
DOI: |
10.3390/e23050517 |
Document Type: |
Journal Article |
Research Program: |
Energiesystemtransformation |
Link: |
Get full text OpenAccess |
Publikationsportal JuSER |
Please use the identifier: http://dx.doi.org/10.3390/e23050517 in citations.
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. |