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

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Abstract

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.

Original languageEnglish
Pages (from-to)62-77
Number of pages16
JournalP-Adic Numbers, Ultrametric Analysis, and Applications
Volume9
Issue number1
DOIs
Publication statusPublished - 2017 Jan 1

Keywords

  • p-adic field
  • semistable law
  • semistable process
  • sum of i.i.d

ASJC Scopus subject areas

  • Mathematics(all)

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