Analysis and data-driven reconstruction of bivariate jump-diffusion processes

Leonardo Rydin Gorjão, Jan Heysel, Klaus Lehnertz, and M. Reza Rahimi Tabar

Phys. Rev. E 100, 062127 – Published 20 December 2019

Abstract

We 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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Received 27 September 2019

DOI:https://doi.org/10.1103/PhysRevE.100.062127

Physics Subject Headings (PhySH)

Diffusion Stochastic processes

Stochastic analysis Stochastic analysis methods Stochastic differential equations

Statistical Physics & Thermodynamics

Authors & Affiliations

Leonardo Rydin Gorjão ^1,2,3,4,*, Jan Heysel ^1,2,†, Klaus Lehnertz ^1,2,5,‡, and M. Reza Rahimi Tabar^6,7,§

¹Department of Epileptology, University of Bonn, Venusberg Campus 1, 53127 Bonn, Germany
²Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany
³Forschungszentrum Jülich, Institute for Energy and Climate Research—Systems Analysis and Technology Evaluation (IEK-STE), 52428 Jülich, Germany
⁴Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany
⁵Interdisciplinary Centre for Complex Systems, University of Bonn, Brühler Straße 7, 53175 Bonn, Germany
⁶Institute of Physics and ForWind, Carl von Ossietzky University of Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26111 Oldenburg, Germany
⁷Department of Physics, Sharif University of Technology, 11365-9161 Tehran, Iran

^*l.rydin.gorjao@fz-juelich.de
^†jan.heysel@uni-bonn.de
^‡klaus.lehnertz@ukbonn.de
^§tabar@uni-oldenburg.de

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Vol. 100, Iss. 6 — December 2019

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