论文标题
在同时限制固定随机INAR（1）过程的限制范围内
On simultaneous limits for aggregation of stationary randomized INAR(1) processes with Poisson innovations
论文作者
论文摘要
我们调查了n个独立的n个独立副本的共同的时间和同时聚集，该副本的n独立副本是第1（inar（1））的n独立副本，其随机系数$α\ in（0,1）$以及具有特殊的Poisson创新。假设$α$具有$ψ（x）（x）（1- x）^β$，$ x \ in（0,1）$的密度函数，带有$β\ in（-1，\ infty）$和$ \ lim_ {x \ lim_ {x \ uparrow 1}ψ（x）ψ（x）ψ（x）= x =ψ_1\ in（x）在所谓的同时情况下，即$ n $和$ n $和时间尺度$ n $以给定的速率以$β$ n $增加。$β\ in（0，\ infty）$保持开放。我们还对共同的分配官方进行有限的分配，该款项仍在（0，\ inftty）中，以$β$β\ in（0，\ infty）的质疑，该汇率以$β\ in（0，\ infty）的质疑，该汇率均以$β$β置于有限的分配中。
We investigate joint temporal and contemporaneous aggregation of N independent copies of strictly stationary INteger-valued AutoRegressive processes of order 1 (INAR(1)) with random coefficient $α\in(0,1)$ and with idiosyncratic Poisson innovations. Assuming that $α$ has a density function of the form $ψ(x) (1 - x)^β$, $x \in (0,1)$, with $β\in(-1,\infty)$ and $\lim_{x\uparrow 1} ψ(x) = ψ_1 \in (0,\infty)$, different limits of appropriately centered and scaled aggregated partial sums are shown to exist for $β\in(-1,0]$ in the so-called simultaneous case, i.e., when both $N$ and the time scale $n$ increase to infinity at a given rate. The case $β\in(0,\infty)$ remains open. We also give a new explicit formula for the joint characteristic functions of finite dimensional distributions of the appropriately centered aggregated process in question.
