Randomly stopped sums with consistently varying distributions
Volume 3, Issue 2 (2016), pp. 165–179
Pub. online: 4 July 2016
Type: Research Article
Open Access
Open Access
Received
13 May 2016
13 May 2016
Accepted
23 June 2016
23 June 2016
Published
4 July 2016
4 July 2016
Abstract
Let $\{\xi _{1},\xi _{2},\dots \}$ be a sequence of independent random variables, and η be a counting random variable independent of this sequence. We consider conditions for $\{\xi _{1},\xi _{2},\dots \}$ and η under which the distribution function of the random sum $S_{\eta }=\xi _{1}+\xi _{2}+\cdots +\xi _{\eta }$ belongs to the class of consistently varying distributions. In our consideration, the random variables $\{\xi _{1},\xi _{2},\dots \}$ are not necessarily identically distributed.
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