On asymptotic scales of independently stopped random sums

Jaakko Lehtomaa

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arXiv · 1405.2239

On asymptotic scales of independently stopped random sums

Jaakko Lehtomaa

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Abstract

We study randomly stopped sums via their asymptotic scales. First, finiteness of moments is considered. To generalise this study, asymptotic scales applicable to the class of all heavy-tailed random variables are used. The stopping is assumed to be independent of the underlying process, which is a random walk. The main result enables one to identify whether the asymptotic behaviour of a stopped sum is dominated by the increment, or the stopping variable. As a consequence of this result, new sufficient conditions for the moment determinacy of compounded sums are obtained.

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Jaakko Lehtomaa. 2014-05-09. On asymptotic scales of independently stopped random sums. https://arxiv.org/abs/1405.2239

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