论文标题
分数skellam过程的非中心偏差
Noncentral moderate deviations for fractional Skellam processes
论文作者
论文摘要
文献中经常使用术语\ emph {中度偏差}表示一类大偏差原理，从某种意义上讲，这些原理填补了概率的收敛性之间的差距（由较大的偏差原理支配）和弱收敛到集中的正态分布之间的差距。当弱收敛是针对非高斯分布时，我们谈论\ emph {非中性中度偏差}。在本文中，我们介绍了文献中两个分数Skellam过程的非中性中度偏差结果（参见Kerss，Leonenko和Sikorskii，2014年）。我们还确定，对于2型的分数Skellam过程（我们可以参考Beghin和Macci中的复合分数泊松过程的最新结果（2022）），零的收敛速度通常更快，因为我们可以证明速率功能之间合适的不平等现象。
The term \emph{moderate deviations} is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability to zero (governed by a large deviation principle) and a weak convergence to a centered Normal distribution. We talk about \emph{noncentral moderate deviations} when the weak convergence is towards a non-Gaussian distribution. In this paper we present noncentral moderate deviation results for two fractional Skellam processes in the literature (see Kerss, Leonenko and Sikorskii, 2014). We also establish that, for the fractional Skellam process of type 2 (for which we can refer the recent results for compound fractional Poisson processes in Beghin and Macci (2022)), the convergences to zero are usually faster because we can prove suitable inequalities between rate functions.
