论文标题
使用真实变量研究固定高斯过程的绕组编号
Studying the winding number for stationary Gaussian processes using real variables
论文作者
论文摘要
我们考虑线上定义的平面固定高斯过程的绕组数量。在轻度条件下，随着时间范围倾向于无穷大，我们获得了绕组数的渐近方差和中央限制定理。在渐近方案中，我们的离散方法等同于文献中先前研究的方法，我们的主要结果扩展了现有方法。我们的模型可以普遍依赖该过程的坐标和其中一个的非差异性。此外，除了我们的一般框架之外，我们认为示例是与坐标既不差异的过程的绕组数的近似值，又是一个不完全固定的过程的绕组数。
We consider the winding number of planar stationary Gaussian processes defined on the line. Under mild conditions, we obtain the asymptotic variance and the Central Limit Theorem for the winding number as the time horizon tends to infinity. In the asymptotic regime, our discrete approach is equivalent to the continuous one studied previously in the literature and our main result extends the existing ones. Our model allows for a general dependence of the coordinates of the process and non-differentiability of one of them. Furthermore, beyond our general framework, we consider as examples an approximation to the winding number of a process whose coordinates are both non-differentiable and the winding number of a process which is not exactly stationary.
