Universität zu Köln

Gorjao, Leonardo Rydin, Heysel, Jan, Lehnertz, Klaus and Tabar, M. Reza Rahimi (2019). Analysis and data-driven reconstruction of bivariate jump-diffusion processes. Phys. Rev. E, 100 (6). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2470-0053

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Gorjao, Leonardo Rydin UNSPECIFIED UNSPECIFIED UNSPECIFIED Heysel, Jan UNSPECIFIED UNSPECIFIED UNSPECIFIED Lehnertz, Klaus UNSPECIFIED UNSPECIFIED UNSPECIFIED Tabar, M. Reza Rahimi UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-124175
DOI:	10.1103/PhysRevE.100.062127
Journal or Publication Title:	Phys. Rev. E
Volume:	100
Number:	6
Date:	2019
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2470-0053
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language NEUTRON-SCATTERING; SYNCHRONIZATION; MODELS; NOISE Multiple languages Physics, Fluids & Plasmas; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/12417