%A Tran Loc HUNG, Phan Tri KIEN %T AN EXTENSION OF ZOLOTAREV'S PROBLEM AND SOME RELATED RESULTS %0 Journal Article %D 2021 %J 数学物理学报(英文版) %R 10.1007/s10473-021-0513-6 %P 1619-1634 %V 41 %N 5 %U {http://121.43.60.238/sxwlxbB/CN/abstract/article_16523.shtml} %8 2021-10-25 %X The main purpose of this paper is to extend the Zolotarev's problem concerning with geometric random sums to negative binomial random sums of independent identically distributed random variables. This extension is equivalent to describing all negative binomial infinitely divisible random variables and related results. Using Trotter-operator technique together with Zolotarev-distance's ideality, some upper bounds of convergence rates of normalized negative binomial random sums (in the sense of convergence in distribution) to Gamma, generalized Laplace and generalized Linnik random variables are established. The obtained results are extension and generalization of several known results related to geometric random sums.