Moderate deviations principle for products of sums of random variables

Abstract

Let (Xn) 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 n k=1 S k n!µ n 1/(γbn √ 2n) , where γ = σ/µ denotes the coefficient of variation and (bn) is the moderate deviations scale. Keywords moderate deviations principle, products of sums, independent identically distribution, positive random variables MSC(2000): 60F10, 60G05 Citation: Miao Y, Mu J Y. Moderate deviations principle for products of sums of random variables.