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 ${X_n: ngeq 1}$; 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 ${rac{1}{log n}sum_{k=1}^nrac{1}{k}X_k:ngeq 1} with speed function $v_n=log n$. We also prove a sample path large deviation principle