具有长记忆的离散拖网过程
Discrete-time trawl processes with long memory
摘要：
我们介绍了一类离散时间平稳拖网过程采取实际或整数值和独立的“种子”过程的收缩间隔（“拖网高度”）的过去值的总和。Barndorff-Nielsen（2011）和Barndorff-Nielsen等人（2014）研究了连续时间内的相关拖网过程，但在我们的情况下，i.i.d.种子过程可以是非常一般的并且不需要是无限可分的。当拖网高度随滞后$j^{-α}$衰减时，对于某些$1< α< 2 $，拖网过程表现出长记忆，其协方差衰减为$j^{1-α}$。我们证明了在一般种子过程的一般条件下，这类拖网过程的归一化部分和既可能趋向于分数布朗运动，也可能趋向于$α$ -稳定的Lévy过程.
英文摘要：
We introduce a class of discrete time stationary trawl processes taking real or integer values and written as sums of past values of independent `seed' processes on shrinking intervals (`trawl heights'). Related trawl processes in continuous time were studied in Barndorff-Nielsen (2011) and Barndorff-Nielsen et al. (2014), however in our case, the i.i.d. seed processes can be very general and need not be infinitely divisible. In the case when the trawl height decays with the lag as $j^{-α}$ for some $1< α< 2 $, the trawl process exhibits long memory and its covariance decays as $j^{1-α}$. We show that under general conditions on generic seed process, the normalized partial sums of such trawl process may tend either to a fractional Brownian motion or to an $α$-stable Lévy process.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
