In this paper we consider several examples of sequences of partial sums of triangular arrays of random variables {X_n: n \geq1}; 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/ logn \sum_{k=1}^n =1/k X_k, n\geq 1} with speed function v_n = logn. We also prove a sample path large deviation principle for {X_n: n \geq 1} defined by X_n(·) = \sum_{i=1}^n U_i (σ^2·)/\sqrt n , where σ^2 ∈ (0,∞) and {U_n: n\geq 1} is a sequence of independent standard Brownian motions.

### Large deviation principles for sequences of logarithmically weighted means

#### Abstract

In this paper we consider several examples of sequences of partial sums of triangular arrays of random variables {X_n: n \geq1}; 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/ logn \sum_{k=1}^n =1/k X_k, n\geq 1} with speed function v_n = logn. We also prove a sample path large deviation principle for {X_n: n \geq 1} defined by X_n(·) = \sum_{i=1}^n U_i (σ^2·)/\sqrt n , where σ^2 ∈ (0,∞) and {U_n: n\geq 1} is a sequence of independent standard Brownian motions.
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2011
Giuliano, Rita; Macci, C.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/146640
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