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.
Giuliano, R., Macci, C. (2011). Large deviation principles for sequences of logarithmically weighted means. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 378(2), 555-570 [10.1016/j.jmaa.2011.01.068].
Large deviation principles for sequences of logarithmically weighted means
MACCI, CLAUDIO
2011-01-01
Abstract
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.| File | Dimensione | Formato | |
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