Limit theorems for p-adic valued asymmetric semistable laws and processes

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• 作者：Kumi Yasuda
• 关键词：Key wordsp ; adic field ; sum of i.i.d. ; semistable law ; semistable process
• 刊名：P-Adic Numbers, Ultrametric Analysis, and Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：9
• 期：1
• 页码：62-77
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra;
• 出版者：Pleiades Publishing
• ISSN：2070-0474
• 卷排序：9

文摘

Limit distributions of scaled sums of p-adic valued i.i.d. are characterized as semistable laws, and a condition to assure the weak convergence of a scaled sum is verified. The limit supremum of the norm of the weakly convergent scaled sum is divergent in fact, and the exact growth rate of the sum is given. It is also shown that, if a scaled sum including a time parameter in the number of the added i.i.d. is considered, the semigroup of the limit distributions corresponds to a p-adic valued Markov process having right continuous sample paths with left limits. These are generalizations of the former results for rotation-symmetric i.i.d., with some necessary modifications.