广义Whittle-Mat $\acute{\text{E}}$ rn随机场作为关联涨落模型
Generalized Whittle-Mat$\acute{\text{E}}$rn random field as a model of correlated fluctuations
摘要：
本文考虑了协方差函数为Whittle-Mat $\acute{\text{e}}$ rn族的高斯随机场的推广.这样一个随机场可以作为具有两个分数阶的分数阶随机微分方程的解而得到。研究了广义Whittle-Mat $\acute{\text{e}}$ rn族中协方差函数的渐近性质，并利用这些协方差函数导出了随机场的样本路径性质. Whittle-Mat $\acute{\text{e}}$ rn场已被广泛用于模拟地质统计数据，如海束数据、风速、场温度和土壤数据。在这篇文章中，我们表明，广义Whittle-Mat $\acute{\text{e}}$ rn场提供了一个更灵活的模型风速数据。
英文摘要：
This paper considers a generalization of Gaussian random field with covariance function of Whittle-Mat$\acute{\text{e}}$rn family. Such a random field can be obtained as the solution to the fractional stochastic differential equation with two fractional orders. Asymptotic properties of the covariance functions belonging to this generalized Whittle-Mat$\acute{\text{e}}$rn family are studied, which are used to deduce the sample path properties of the random field. The Whittle-Mat$\acute{\text{e}}$rn field has been widely used in modeling geostatistical data such as sea beam data, wind speed, field temperature and soil data. In this article we show that generalized Whittle-Mat$\acute{\text{e}}$rn field provides a more flexible model for wind speed data.
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