论文标题
与分数高斯噪声有关的分析和计算问题
Analytical and computational problems related to fractional Gaussian noise
论文作者
论文摘要
我们研究了分数高斯噪声元素在其相邻元素上的投影。我们证明了该投影系数的一些分析结果，特别是我们为它们获得了复发关系。我们还对这些系数的行为做出了几种猜想，提供了支持这些猜想的数值证据，并在理论上研究了这些猜想。作为独立利益的辅助结果，我们研究了分数高斯噪声的协方差函数，证明它完全单调为$ h> 1/2 $，特别是单调的，凸面，log-convex，以及进一步的有用属性。
We study the projection of an element of fractional Gaussian noise onto its neighbouring elements. We prove some analytic results for the coefficients of this projection, in particular, we obtain recurrence relations for them. We also make several conjectures concerning the behaviour of these coefficients, provide numerical evidence supporting these conjectures, and study them theoretically in particular cases. As an auxiliary result of independent interest, we investigate the covariance function of fractional Gaussian noise, prove that it is completely monotone for $H>1/2$, and, in particular monotone, convex, log-convex along with further useful properties.
