This paper discusses a statistical method of detecting nonlinearity in the light curves of active galactic nuclei (AGN). We model the light curves of AGN by two-variate stochastic differential equation (SDE) in which one variable is observable but not the other. Applying a nonparametric model of the SDE as well as its parametric models of linear and quadratic functions to the light curves provided by the Kepler satellite, we estimate the three models and thereby compare their prediction accuracy to detect nonlinearity. The results suggest that there exist quadratic or other nonlinearities in the light curves, while the others exhibit linearity.

中文翻译：

---

检测活跃银河原子核光曲线的非线性

本文讨论了一种统计方法，用于检测活动银河核（AGN）光曲线中的非线性。我们通过二变量随机微分方程（SDE）对AGN的光曲线进行建模，其中一个变量是可观测的，而另一个变量则不可观测。将SDE的非参数模型及其线性和二次函数的参数模型应用于开普勒卫星提供的光曲线，我们估计了这三个模型，从而比较了它们的预测精度以检测非线性。结果表明，在光曲线中存在二次或其他非线性，而其他呈现线性。