Research output: Contribution to journal › Article › peer-review
Strong limit theorems for increments of renewal processes. / Frolov, A. N.
In: Journal of Mathematical Sciences , Vol. 128, No. 1, 07.2005, p. 2614-2624.Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - Strong limit theorems for increments of renewal processes
AU - Frolov, A. N.
N1 - Funding Information: This research was partially supported by the Ministry of Education of the RF (project E02-1.0-56). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2005/7
Y1 - 2005/7
N2 - We study the almost sure behavior of increments of renewal processes. We derive a universal form of norming functions in the strong limit theorems for increments of such processes. This result unifies the following well-known theorems for increments of renewal processes: the strong law of large numbers, Erdos-Renyi law, Csorgo-Revesz law, and law of the iterated logarithm. New results are obtained for processes with distributions of renewal times from domains of attraction of the normal law and completely asymmetric stable laws with index α (1, 2). Bibliography: 15 titles.
AB - We study the almost sure behavior of increments of renewal processes. We derive a universal form of norming functions in the strong limit theorems for increments of such processes. This result unifies the following well-known theorems for increments of renewal processes: the strong law of large numbers, Erdos-Renyi law, Csorgo-Revesz law, and law of the iterated logarithm. New results are obtained for processes with distributions of renewal times from domains of attraction of the normal law and completely asymmetric stable laws with index α (1, 2). Bibliography: 15 titles.
UR - http://www.scopus.com/inward/record.url?scp=21544474710&partnerID=8YFLogxK
U2 - 10.1007/s10958-005-0210-3
DO - 10.1007/s10958-005-0210-3
M3 - Article
AN - SCOPUS:21544474710
VL - 128
SP - 2614
EP - 2624
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 1
ER -
ID: 75022007