Department of Epileptology, University of Bonn, Venusberg Campus 1, 53127 Bonn, Germany.
Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany.
Phys Rev E. 2019 Dec;100(6-1):062127. doi: 10.1103/PhysRevE.100.062127.
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.
我们引入了双变量跳跃扩散过程，它由二维扩散和二维跳跃组成，可以相互耦合。我们提出了一种数据驱动的、非参数的高阶（高达 8 阶）Kramers-Moyal 系数估计方法，该方法可以重建潜在跳跃扩散过程的相关方面，并恢复潜在参数。该方法使用连续和不连续过程的合成双变量时间序列，通过数值集成数据进行了验证。我们进一步评估了通过数据驱动的高阶 Kramers-Moyal 系数分析来估计跳跃扩散模型参数的可能性，以及数据中点数不足或系统参数不成比例带来的限制。
