论文标题
分数集成的移动平均稳定过程，具有远程依赖性
Fractionally Integrated Moving Average Stable Processes With Long-Range Dependence
论文作者
论文摘要
在文献中，对莱维噪声驱动的长期记忆过程已经得到了很好的研究。它们形成了非常丰富的流程类，表现出像功能功能一样衰减的自动助力功能。在这里，我们研究了一类Lévy过程，其二阶时刻是无限的，即所谓的$α$稳定过程。基于Samorodnitsky和Taqqu（2000），我们构建了一个等轴测图，使我们能够使用Riemann-Liouville分数积分来定义有关线性分数稳定运动的随机积分。通过这种结构，自然会按零件公式进行整合。然后，我们使用一般性措施来研究其依赖性结构，以远程依赖的特性提出一个固定$SαS$过程的家族。最后，在一个时间样本中，大量结果的定律显示为等轴测图和按零件公式进行集成的应用。
Long memory processes driven by Lévy noise with finite second-order moments have been well studied in the literature. They form a very rich class of processes presenting an autocovariance function which decays like a power function. Here, we study a class of Lévy process whose second-order moments are infinite, the so-called $α$-stable processes. Based on Samorodnitsky and Taqqu (2000), we construct an isometry that allows us to define stochastic integrals concerning the linear fractional stable motion using Riemann-Liouville fractional integrals. With this construction, follows naturally an integration by parts formula. We then present a family of stationary $SαS$ processes with the property of long-range dependence, using a generalized measure to investigate its dependence structure. In the end, the law of large number's result for a time's sample of the process is shown as an application of the isometry and integration by parts formula.
