Precise large deviations for the difference of two sums of WUOD and non identically distributed random variables with dominatedly varying tails

Lixin Song, Zhiqiang Hua, Dawei Lu and Xiaomeng Qi

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 4, 2013-2028

Abstract: In this article, we study large deviations for non random difference ∑n1(t)j = 1X1j − ∑n2(t)j = 1X2j and random difference ∑N1(t)j = 1X1j − ∑N2(t)j = 1X2j, where {X1j, j ⩾ 1} is a sequence of widely upper orthant dependent (WUOD) random variables with non identical distributions {F1j(x), j ⩾ 1}, {X2j, j ⩾ 1} is a sequence of independent identically distributed random variables, n1(t) and n2(t) are two positive integer-valued functions, and {Ni(t), t ⩾ 0}2i = 1 with ENi(t) = λi(t) are two counting processes independent of {Xij, j ⩾ 1}2i = 1. Under several assumptions, some results of precise large deviations for non random difference and random difference are derived, and some corresponding results are extended.

Date: 2017
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DOI: 10.1080/03610926.2015.1032424

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