TY - JOUR

T1 - Limit theorems for p-adic valued asymmetric semistable laws and processes

AU - Yasuda, Kumi

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - p-adic field

KW - semistable law

KW - semistable process

KW - sum of i.i.d

UR - http://www.scopus.com/inward/record.url?scp=85012216773&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85012216773&partnerID=8YFLogxK

U2 - 10.1134/S207004661701006X

DO - 10.1134/S207004661701006X

M3 - Article

AN - SCOPUS:85012216773

VL - 9

SP - 62

EP - 77

JO - P-Adic Numbers, Ultrametric Analysis, and Applications

JF - P-Adic Numbers, Ultrametric Analysis, and Applications

SN - 2070-0466

IS - 1

ER -