Large deviation principles for sequences of logarithmically weighted means

In this paper we consider several examples of sequences of partial sums of triangular arrays of random variables {X-n: n >= 1}: in each case X-n converges weakly to an infinitely divisible distribution (a Poisson distribution or a centered Normal distribution). For each sequence we prove large deviation results for the logarithmically weighted means {1/lobn Sigma(n)(k=1) 1/k X-k: n >= 1) with speed function v(n) = logn. We also prove a sample path large {deviation principle for {X-n: n >= 1) defined by X-n(.) = Sigma i=iUi(sigma(2) .)/root n where sigma(2) is an element of (0, infinity) and {Un: n >= .1} is a sequence of independent standard Brownian motions. (C) 2011 Elsevier Inc. All rights reserved.