Randomly stopped sums with consistently varying distributions

• Main Authors: Edita Kizinevič, Jonas Sprindys, Jonas Šiaulys
• Format: Article
• Language: English
• Published: VTeX 2016-07-01
• Series: Modern Stochastics: Theory and Applications
• Subjects: Heavy tail; consistently varying tail; randomly stopped sum; inhomogeneous distributions; convolution closure; random convolution closure
• Online Access: https://vmsta.vtex.vmt/doi/10.15559/16-VMSTA60

Let $\{\xi _{1},\xi _{2},\dots \}$ be a sequence of independent random variables, and η be a counting random variable independent of this sequence. We consider conditions for $\{\xi _{1},\xi _{2},\dots \}$ and η under which the distribution function of the random sum $S_{\eta }=\xi _{1}+\xi _{2}+\cdots +\xi _{\eta }$ belongs to the class of consistently varying distributions. In our consideration, the random variables $\{\xi _{1},\xi _{2},\dots \}$ are not necessarily identically distributed.