Large deviation principles for sequences of logarithmically weighted means |
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Authors: | Rita Giuliano |
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Institution: | a Dipartimento di Matematica “L. Tonelli”, Università di Pisa, Largo Bruno Pontecorvo 5, I-56127 Pisa, Italy b Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, I-00133 Rome, Italy |
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Abstract: | In this paper we consider several examples of sequences of partial sums of triangular arrays of random variables {Xn:n?1}; in each case Xn 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 with speed function . We also prove a sample path large deviation principle for {Xn:n?1} defined by , where σ2∈(0,∞) and {Un:n?1} is a sequence of independent standard Brownian motions. |
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Keywords: | Large deviations Logarithmically weighted mean Almost sure central limit theorem Triangular array Infinitely divisible distribution Hellinger distance |
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