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000873131 0247_ $$2doi$$a10.1103/PhysRevE.100.062127
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000873131 1001_ $$0P:(DE-Juel1)173608$$aRydin Gorjão, Leonardo$$b0$$eCorresponding author
000873131 245__ $$aAnalysis and data-driven reconstruction of bivariate jump-diffusion processes
000873131 260__ $$aWoodbury, NY$$bAPS$$c2019
000873131 264_1 $$2Crossref$$3online$$bAmerican Physical Society (APS)$$c2019-12-20
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000873131 520__ $$aWe introduce the bivariate jump-diffusion process, consisting of two-dimensional diffusion and two-dimensional jumps, that can be coupled to one another. We present a data-driven, nonparametric estimation procedure of higher-order (up to 8) Kramers-Moyal coefficients that allows one to reconstruct relevant aspects of the underlying jump-diffusion processes and to recover the underlying parameters. The procedure is validated with numerically integrated data using synthetic bivariate time series from continuous and discontinuous processes. We further evaluate the possibility of estimating the parameters of the jump-diffusion model via data-driven analyses of the higher-order Kramers-Moyal coefficients, and the limitations arising from the scarcity of points in the data or disproportionate parameters in the system.
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000873131 7001_ $$00000-0003-3395-1008$$aHeysel, Jan$$b1
000873131 7001_ $$00000-0002-5529-8559$$aLehnertz, Klaus$$b2
000873131 7001_ $$0P:(DE-HGF)0$$aTabar, M. Reza Rahimi$$b3
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