论文标题
限制随机场的多归因产物定理
Limit theorems for multifractal products of random fields
论文作者
论文摘要
本文研究了随机场的多重分子产物的渐近特性。获得的限制定理为空间中的累积字段的收敛提供了足够的条件。$ $ l_q。$新的结果介绍了累积场收敛速率。给出了极限定理的简单统一条件和Rényi函数的计算。它们的限制性不如已知的一维结果中的限制性。开发的方法也适用于多维多效测量。最后，提出了一类新的几何$φ$ -SUB-GAUSSIAN随机字段的示例。在这种情况下，一般假设具有简单的形式，只能以协方差函数来表示。
This paper investigates asymptotic properties of multifractal products of random fields. The obtained limit theorems provide sufficient conditions for the convergence of cumulative fields in the spaces $L_q.$ New results on the rate of convergence of cumulative fields are presented. Simple unified conditions for the limit theorems and the calculation of the Rényi function are given. They are less restrictive than those in the known one-dimensional results. The developed methodology is also applied to multidimensional multifractal measures. Finally, a new class of examples of geometric $φ$-sub-Gaussian random fields is presented. In this case, the general assumptions have a simple form and can be expressed in terms of covariance functions only.
