论文标题
最小二乘估计器基于ADAMS方法的随机微分方程，其lévy噪声小
Least squares estimators based on the Adams method for stochastic differential equations with small Lévy noise
论文作者
论文摘要
我们考虑由带有一些未知参数的小lévy噪声驱动的随机微分方程（SDE），并根据SDES的离散样品提出了一种新型的最小二乘估计器。为了近似从SDE中的过程的增量，我们不使用通常的Euler方法，而是ADAMS方法，即对解决方案的众所周知的数值近似值出现在SDE极限中的普通微分方程。我们显示了提出的估计器以及合适的观察方案中提出的渐近分布的一致性。我们还表明，根据有限样本性能，基于Euler方法，我们的估计器可以比通常的LSE更好。
We consider stochastic differential equations (SDEs) driven by small Lévy 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.
