A. A. Borovkov, “Integral theorems for the first passage time of an arbitrary boundary by a compound renewal process”, Sibirsk. Mat. Zh., 2015, Volume 56, Number 5,Pages <nobr>961

This article is cited in 1 paper

Integral theorems for the first passage time of an arbitrary boundary by a compound renewal process

A. A. Borovkov^ab

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Abstract: We obtain the integral limit theorems for the first passage time through an arbitrary remote boundary by a compound renewal process both for the cases of finite and infinite variance of the process. In the latter case, we assume that some distributions belong to the attraction domain of the stable law.

Keywords: compound renewal process, first passage time through an arbitrary boundary, law of the iterated logarithm, analog of the law of the iterated logarithm in the case of infinite variance.

UDC: 519.21

Received: 01.06.2015

DOI: 10.17377/smzh.2015.56.501