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• W3159343572 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." @default.
• W3159343572 created "2021-05-10" @default.
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• W3159343572 date "2021-04-24" @default.
• W3159343572 modified "2023-10-02" @default.
• W3159343572 title "Arbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator" @default.
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• W3159343572 doi "https://doi.org/10.3390/e23050517" @default.
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