We consider stochastic differential equations (SDEs) driven by small L\'evy noise with some unknown parameters, and propose a new type of least squares estimators based on discrete samples from the SDEs. To approximate the increments of a process from the SDEs, we shall use not the usual Euler method, but the Adams method, that is, a well-known numerical approximation of the solution to the ordinary differential equation appearing in the limit of the SDE. We show the consistency of the proposed estimators as well as the asymptotic distribution in a suitable observation scheme. We also show that our estimators can be better than the usual LSE based on the Euler method in the finite sample performance.
翻译：我们考虑的是由小L\'evy噪声驱动的随机差异方程式(SDEs),它有一些未知参数,我们根据SDEs的离散样本提出了新型最小方位估计器。为了比照SDEs的进程增量,我们不应使用通常的 Euler 方法,而应使用Adams 方法,即众所周知的SDE 极限中普通差异方程解决办法的数字近似值。我们显示了拟议估计器的一致性以及适当观测计划中的孔隙分布。我们还表明,根据有限样本性能中的 Euler 方法,我们的估计器可能比通常的 LSE值更好。
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