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

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  • Lixin Song
  • Zhiqiang Hua
  • Dawei Lu
  • Xiaomeng Qi

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.

Suggested Citation

  • Lixin Song & Zhiqiang Hua & Dawei Lu & Xiaomeng Qi, 2017. "Precise large deviations for the difference of two sums of WUOD and non identically distributed random variables with dominatedly varying tails," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(4), pages 2013-2028, February.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:4:p:2013-2028
    DOI: 10.1080/03610926.2015.1032424
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