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Moderate deviations principle for products of sums of random variables

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Abstract

Let (X n )n ⩾ 1 be a sequence of independent identically distributed (i.i.d.) positive random variables with EX 1 = µ, Var(X 1) = σ 2. In the present paper, we establish the moderate deviations principle for the products of partial sums

$$ \left( {\frac{{\prod _{k = 1}^n S_k }} {{n!\mu ^n }}} \right)^{{1 \mathord{\left/ {\vphantom {1 {\left( {\gamma b_n \sqrt {2n} } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\gamma b_n \sqrt {2n} } \right)}}} , $$

where γ = σ/µ denotes the coefficient of variation and (b n ) is the moderate deviations scale.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Yu Miao & JianYong Mu

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  1. Yu Miao
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  2. JianYong Mu
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Correspondence to Yu Miao.

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Miao, Y., Mu, J. Moderate deviations principle for products of sums of random variables. Sci. China Math. 54, 769–784 (2011). https://doi.org/10.1007/s11425-011-4195-8

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  • DOI: https://doi.org/10.1007/s11425-011-4195-8

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