Randomly stopped sums with consistently varying distributions

Let $\{ξ_1,ξ_2,\ldots\}$ be a sequence of independent random variables, and $η$ be a counting random variable independent of this sequence. We consider conditions for $\{ξ_1,ξ_2,\ldots\}$ and $η$ under which the distribution function of the random sum $S_η=ξ_1+ξ_2+\cdots+ξ_η$ belongs to the class of consistently varying distributions. In our consideration, the random variables $\{ξ_1,ξ_2,\ldots\}$ are not necessarily identically distributed.

No reviews yet.

No comments yet.