论文标题
再生成分中等零件：常规变化的情况
Moderate parts in regenerative compositions: the case of regular variation
论文作者
论文摘要
整数$ n $的再生随机组成是通过分配$ n $标准指数积分在可数的间隔数中构建的，其中包括下属$ s $的封闭范围的补充。 Assuming that the Lévy measure of $S$ is infinite and regularly varying at zero of index $-α$, $α\in(0,\,1)$, we find an explicit threshold $r=r(n)$, such that the number $K_{n,\,r(n)}$ of blocks of size $r(n)$ converges in distribution without any normalization to a mixed Poisson distribution.序列$（r（n））$ juart定期随索引$α/（α+1）$变化，混合分布是$ s $的指数函数的。结果是由于通用泊松限制了无限占用方案的总定理的结果，并具有频率的功率衰减。我们还讨论$ k_ {n，\，w（n）} $的渐近行为，当$ w（n）$ diverges但增长慢于$ r（n）$时。我们的发现补充了以前已知的大数字法律，以$ k_ {n，\，r} $在\ mathbb {n} $中固定的$ r \。作为一个关键工具，我们采用新的Abelian定理来进行拉普拉斯 - StileTjes会随着规则变化的索引变化的定期变化而变化，定期变化。
A regenerative random composition of integer $n$ is constructed by allocating $n$ standard exponential points over a countable number of intervals, comprising the complement of the closed range of a subordinator $S$. Assuming that the Lévy measure of $S$ is infinite and regularly varying at zero of index $-α$, $α\in(0,\,1)$, we find an explicit threshold $r=r(n)$, such that the number $K_{n,\,r(n)}$ of blocks of size $r(n)$ converges in distribution without any normalization to a mixed Poisson distribution. The sequence $(r(n))$ turns out to be regularly varying with index $α/(α+1)$ and the mixing distribution is that of the exponential functional of $S$. The result is derived as a consequence of a general Poisson limit theorem for an infinite occupancy scheme with power-like decay of the frequencies. We also discuss asymptotic behavior of $K_{n,\,w(n)}$ in cases when $w(n)$ diverges but grows slower than $r(n)$. Our findings complement previously known strong laws of large numbers for $K_{n,\,r}$ in case of a fixed $r\in\mathbb{N}$. As a key tool we employ new Abelian theorems for Laplace--Stiletjes transforms of regularly varying functions with the indexes of regular variation diverging to infinity.
