Regularly distributed randomly stopped sum, minimum, and maximum
Articles
Jonas Sprindys
Vilnius University
Jonas Šiaulys
Vilnius University
https://orcid.org/0000-0002-8480-5644
Published 2020-05-01
https://doi.org/10.15388/namc.2020.25.16661
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Keywords

regularly varying distribution
counting random variable
randomly stopped maximum
randomly stopped minimum
randomly stopped sum
closure property

How to Cite

SprindysJ. and ŠiaulysJ. (2020) “Regularly distributed randomly stopped sum, minimum, and maximum”, Nonlinear Analysis: Modelling and Control, 25(3), pp. 509–522. doi: 10.15388/namc.2020.25.16661.

Abstract

Let {ξ1,ξ2,...} be a sequence of independent real-valued, possibly nonidentically distributed, random variables, and let η be a nonnegative, nondegenerate at 0, and integer-valued random variable, which is independent of {ξ1,ξ2,...}. We consider conditions for {ξ1,ξ2,...} and η under which the distributions of the randomly stopped minimum, maximum, and sum are regularly varying.

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