Asymptotically correct bounds of geometric convolutions with subexponential components
Let \(F\) be a subexponential distribution in the sense of \textit{Chistyakov} [Teor. Veroyatn. Primen. 9, 640-648 (1964)]. The authors gives sharp bounds for the asymptotics at infinity of the so-called geometric convolution \(T(x)\). Here \(T(x) = q \sum_{k=1}^{\infty} {(1-q)}(1-F_k(x))\), where \(F_k\) is the \(k\)-fold convolution of \(F\).
scientific article; zbMATH DE number 1756324