无正则变差时的强更新定理和局部极限定理
Strong renewal theorem and local limit theorem in the absence of regular variation
摘要：
当底层分布属于几何部分吸引域时，得到了一个强更新定理，其平均值超过正则变分的无穷大，并且是一个指数为$α\in (1/2,1]$的半稳定律.在这个过程中，我们得到了局部极限定理的有限和无限的平均，即整个范围$α\in (0,2)$。我们还导出了$α\in (0,1]$更新函数的渐近性。
英文摘要：
We obtain a strong renewal theorem with infinite mean beyond regular variation, when the underlying distribution belongs to the domain of geometric partial attraction a semistable law with index $α\in (1/2,1]$. In the process we obtain local limit theorems for both finite and infinite mean, that is for the whole range $α\in (0,2)$. We also derive the asymptotics of the renewal function for $α\in (0,1]$.
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。
