TY  - JOUR
AU  - Rydin Gorjão, Leonardo
AU  - Heysel, Jan
AU  - Lehnertz, Klaus
AU  - Tabar, M. Reza Rahimi
TI  - Analysis and data-driven reconstruction of bivariate jump-diffusion processes
JO  - Physical review / E
VL  - 100
IS  - 6
SN  - 2470-0045
CY  - Woodbury, NY
PB  - APS
M1  - FZJ-2020-00576
SP  - 062127
PY  - 2019
AB  - 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.
LB  - PUB:(DE-HGF)16
C6  - pmid:31962437
UR  - <Go to ISI:>//WOS:000503814600003
DO  - DOI:10.1103/PhysRevE.100.062127
UR  - https://juser.fz-juelich.de/record/873131
ER  -