Abstract
Let X, Xn, n ≥ 1 be a sequence of iid real random variables, and , n ≥ 1. Convergence rates of moderate deviations are derived, i.e., the rate of convergence to zero of certain tail probabilities of the partial sums are determined. For example, we obtain equivalent conditions for the convergence of series only under the assumptions convergence that EX = 0 and EX2 = 1, where φ and ψ are taken from a broad class of functions. These results generalize and improve some recent results of Li (1991) and Gafurov (1982) and some previous work of Davis (1968). For b ∈ [0, 1] and ϵ > 0, let urn:x-wiley:01611712:media:ijmm792893:ijmm792893-math-0003 The behaviour of Eλϵ,b as ϵ ↓ 0 is also studied.
Highlights
Xn, Let X, nR1 be id random variables with EX 0 and EX I
Let X Xn r.l be a sequence of id random variables with
Let X, Xn, nl be a EXI([X sequence of lid random variables with EX O, EX 1, and t)
Summary
Let X, nR1 be id random variables with EX 0 and EX I. Davis (1968), Theorem 3, p.1483 proved the following result. Theorem 2.1 is a very general result from which quite a number of results in the literature follow as special cases. Some classical results follow as special cases of Theorem 2.1.
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More From: International Journal of Mathematics and Mathematical Sciences
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