Randomly stopped maximum and maximum of sums with consistently varying distributions

Ieva Marija Andrulytė, Martynas Manstavičius, Jonas Šiaulys

Let $\{{\xi }_1,{\xi }_2,\dots \}$ be a sequence of independent random variables, and $\eta$ be a counting random variable independent of this sequence. In addition, let $S_0:=0$ and $S_n:=ξ_1+…