英文文献:On critical cases in limit theory for stationary increments Lévy driven moving averages-静态增量驱动移动平均线的极限理论的临界情况
英文文献作者:Andreas Basse-O'Connor,Mark Podolskij
英文文献摘要:
In this paper we present some limit theorems for power variation of stationary increments Lévy driven moving averages in the setting of critical regimes. In [5] the authors derived first and second order asymptotic results for k-th order increments of stationary increments Lévy driven moving averages. The limit theory heavily depends on the interplay between the given order of the increments, the considered power, the Blumenthal-Getoor index of the driving pure jump Lévy process L and the behavior of the kernel function g at 0. In this work we will study the critical cases, which were not covered in the original work [5].
本文给出了在临界状态的设定下,平稳增量和驱动移动平均的功率变化的一些极限定理。在[5]中,作者推导了平稳增量的k阶增量的一阶和二阶渐近结果。极限理论在很大程度上依赖于增量的给定阶数、考虑的幂次、驱动纯跳跃Levy过程的Blumenthal-Getoor指数与核函数g在0点处的行为之间的相互作用。在这项工作中,我们将研究在原始工作[5]中没有涉及到的关键案例。