Randomly stopped sums of not identically distributed heavy tailed random variables

Let {ξ1,ξ2,…}{ξ1,ξ2,…} be a sequence of independent but not necessarily identically distributed non-negative random variables a number of which has distribution functions with dominatingly varying tails. Let ηη be a counting random variable independent of {ξ1,ξ2,…}{ξ1,ξ2,…}. We consider conditions for random variables {ξ1,ξ2,…}{ξ1,ξ2,…} and ηη under which distribution of the random sum ξ1+ξ2+⋯+ξηξ1+ξ2+⋯+ξη preserves dominatingly varying tail.