Winding number for stationary Gaussian processes using real variables

IF 1.5 Q2 PHYSICS, MATHEMATICAL
J.-M. Azaïs, F. Dalmao, J. R. León
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引用次数: 0

Abstract

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 number of winding turns 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.
使用实变量的平稳高斯过程的圈数
我们考虑在直线上定义的平面平稳高斯过程的圈数。在温和的条件下,我们得到了当时间视界趋于无穷时绕组匝数的渐近方差和中心极限定理。在渐近区域,我们的离散方法等价于先前文献中研究的连续方法,我们的主要结果扩展了已有的结果。我们的模型允许过程坐标的一般依赖性和其中一个的不可微性。此外,在我们的一般框架之外,我们考虑了坐标不可微过程的圈数近似和非完全平稳过程的圈数的例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
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