Journal of University of Science and Technology of China ›› 2019, Vol. 49 ›› Issue (5): 390-396.DOI: 10.3969/j.issn.0253-2778.2019.05.006
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GUO Duo
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Abstract: Let X={X1,X2,…} be a sequence of independent but not necessarily identically distributed random variables,and let η be an integer-valued counting random variable independent of X .Random sum Sη=∑ηk=1 Xk and its maximum S(η)=max{S0,…,Sη} were studied. Assuming that each Xk belongs to the class of D , by using the result of the precise large deviation principles on class D , it was proven that the distributions of Sη and S(η) belong to the same class under some conditions.The obtained results expand the related ones of previous studies.
Key words: random sum, random maximum, precise large deviation, closure property
GUO Duo, HANG Min, WANG Shijie. Closure property of random sum and its maximum of random variables from class D based on precise large deviation principles[J]. Journal of University of Science and Technology of China, 2019, 49(5): 390-396.
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URL: http://just-cn.ustc.edu.cn/EN/10.3969/j.issn.0253-2778.2019.05.006
http://just-cn.ustc.edu.cn/EN/Y2019/V49/I5/390