Abstract
Let {X n ; n ≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E(X 1) and let {N(t); t ≥ 0} be a random process taking non-negative integer values with finite mean λ(t) = E(N(t)) and independent of {X n ; n ≥ 1}. In this paper, asymptotic expressions of P((X 1+⋯+X N(t))−λ(t)μ > x) uniformly for x ∈ [γb(t),∞) are obtained, where γ > 0 and b(t) can be taken to be a positive function with lim t →∞ b(t)/λ(t) = 0.
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Research supported by NSFC (No. 10271091, 10571139)
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Gao, F.Q. Moderate Deviations for Random Sums of Heavy-Tailed Random Variables. Acta Math Sinica 23, 1527–1536 (2007). https://doi.org/10.1007/s10114-007-0941-9
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DOI: https://doi.org/10.1007/s10114-007-0941-9