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000891975 1001_ $$0P:(DE-Juel1)173608$$aRydin Gorjão, Leonardo$$b0$$eCorresponding author
000891975 245__ $$aArbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator
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000891975 520__ $$aWith 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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000891975 7001_ $$0P:(DE-Juel1)162277$$aWitthaut, Dirk$$b1
000891975 7001_ $$00000-0002-5529-8559$$aLehnertz, Klaus$$b2
000891975 7001_ $$00000-0002-8176-666X$$aLind, Pedro G.$$b3
000891975 773__ $$0PERI:(DE-600)2014734-X$$a10.3390/e23050517$$gVol. 23, no. 5, p. 517 -$$n5$$p517 -$$tEntropy$$v23$$x1099-4300$$y2021
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