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We evaluate the significance of a recently proposed bivariate jump-diffusionmodel for a data-driven characterization of interactions between complexdynamical systems. For various coupled and non-coupled jump-diffusionprocesses, we find that the inevitably finite sampling interval of time-seriesdata negatively affects the reconstruction accuracy of higher-order conditionalmoments that are required to reconstruct the underlying jump-diffusionequations. We derive correction terms for conditional moments in higher ordersof the sampling interval and demonstrate their suitability to strongly enhancethe data-driven reconstruction accuracy.

journal of statistical mechanics

Enhancing the accuracy of a data-driven reconstruction of bivariate  jump-diffusion models with corrections for higher orders of the sampling  interval