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Arbitrary-Order Finite-Time Corrections for the Kramers–Moyal Operator.
- Source :
-
Entropy . May2021, Vol. 23 Issue 5, p517. 1p. - Publication Year :
- 2021
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10994300
- Volume :
- 23
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Entropy
- Publication Type :
- Academic Journal
- Accession number :
- 150474880
- Full Text :
- https://doi.org/10.3390/e23050517