| Title | Randomly stopped maximum and maximum of sums with consistently varying distributions / |
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| Authors | Andrulytė, Ieva Marija ; Manstavičius, Martynas ; Šiaulys, Jonas |
| DOI | 10.15559/17-VMSTA74 |
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| Is Part of | Modern stochastics: theory and applications.. Vilnius; Kiev : VTeX. 2017, Vol. 4, no 1, p. 65-78.. ISSN 2351-6054 |
| Keywords [eng] | Heavy tail ; consistently varying tail ; randomly stopped maximum ; randomly stopped maximum of sums ; closure property |
| Abstract [eng] | Let {ξ 1 ,ξ 2 ,...} be a sequence of independent random variables, and η be a count- ing random variable independent of this sequence. In addition, let S 0 := 0 and S n := ξ 1 + ξ 2 +···+ξ n for n ? 1. We consider conditions for random variables {ξ 1 ,ξ 2 ,...} and η under which the distribution functions of the random maximum ξ (η) := max{0,ξ 1 ,ξ 2 ,...,ξ η } and of the random maximum of sums S (η) := max{S 0 ,S 1 ,S 2 ,...,S η } belong to the class of con- sistently varying distributions. . In our consideration the random variables {ξ 1 ,ξ 2 ,...} are not necessarily identically distributed. |
| Published | Vilnius; Kiev : VTeX |
| Type | Journal article |
| Language | English |
| Publication date | 2017 |