论文标题
分数类型的功率变化无限分开的随机场
Power variations for fractional type infinitely divisible random fields
论文作者
论文摘要
本文介绍了针对分数类型对称无限分开的随机场的功率变化的新限制定理。更具体地说，随机字段$ x =（x（\ boldsymbol {t}））_ {\ boldsymbol {t} \ in [0,1]^d} $在[0,1]^d} $ in [0,1]^d} $中定义为kernel函数$ g $相对于对称的无限无限的随机度量的$ l $ l $ l $ l $ l $ l $ n和mess $ n $ n n n $ n n $ n^$ n^。作为$ n \ to \ infty $，对于从$ x $的矩形增量构建的功率变化统计量获得了一阶限制。目前的工作主要与Basse-O'Connor，Lachièze-Rey，Podolskij（2017），Basse-O'Connor，Heinrich，Podolskij（2019）有关，后者在情况中研究了类似的问题$ d = 1 $。但是，我们将看到，与Basse-O'Connor，Lachièze-Rey，Podolskij（2017），Basse-O'Connor，Heinrich，Heinrich，Podolskij（2019）相比，随机场设置中的渐近理论要丰富得多，因为它具有新的限制，包括新的限制，这些限制取决于精确的结构。我们将提供一些重要的例子，包括Lévy移动平均场，均衡的对称线性线性分数$β$稳定纸以及移动平均值分数$β$ - 稳定场，并讨论统计推断的潜在后果。
This paper presents new limit theorems for power variation of fractional type symmetric infinitely divisible random fields. More specifically, the random field $X = (X(\boldsymbol{t}))_{\boldsymbol{t} \in [0,1]^d}$ is defined as an integral of a kernel function $g$ with respect to a symmetric infinitely divisible random measure $L$ and is observed on a grid with mesh size $n^{-1}$. As $n \to \infty$, the first order limits are obtained for power variation statistics constructed from rectangular increments of $X$. The present work is mostly related to Basse-O'Connor, Lachièze-Rey, Podolskij (2017), Basse-O'Connor, Heinrich, Podolskij (2019), who studied a similar problem in the case $d=1$. We will see, however, that the asymptotic theory in the random field setting is much richer compared to Basse-O'Connor, Lachièze-Rey, Podolskij (2017), Basse-O'Connor, Heinrich, Podolskij (2019) as it contains new limits, which depend on the precise structure of the kernel $g$. We will give some important examples including the Lévy moving average field, the well-balanced symmetric linear fractional $β$-stable sheet, and the moving average fractional $β$-stable field, and discuss potential consequences for statistical inference.
