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Teor. Veroyatnost. i Primenen., 2018, Volume 63, Issue 4, Pages 779–794 (Mi tvp5149)  

Limit theorems for random exponentials: the bounded support case

M. Grabchaka, S. A. Molchanovab

a Department of Mathematics and Statistics, University of North Carolina Charlotte, Charlotte, NC, USA
b National Research University Higher School of Economics, Moscow

Abstract: In this paper we study the asymptotic distributions, under appropriate normalization, of the sum $S_t = \sum_{i=1}^{N_t} e^{t X_i}$, the maximum $M_t = \max_{i\in\{1,2,…,N_t\}} e^{tX_i}$, and the $l_t$ norm $R_t=S_t^{1/t}$, when $N_t\to\infty$ as $t\to\infty$ and $X_1,X_2,…$ are independent and identically distributed random variables in the maximum domain of attraction of the reverse-Weibull distribution.

Keywords: random exponentials, exponential sums, random energy model.

Funding Agency Grant Number
Russian Science Foundation 17-11-01098


DOI: https://doi.org/10.4213/tvp5149

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English version:
Theory of Probability and its Applications, 2019, 63:4, 634–647

Bibliographic databases:

Received: 11.07.2017
Accepted:05.04.2018

Citation: M. Grabchak, S. A. Molchanov, “Limit theorems for random exponentials: the bounded support case”, Teor. Veroyatnost. i Primenen., 63:4 (2018), 779–794; Theory Probab. Appl., 63:4 (2019), 634–647

Citation in format AMSBIB
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\pages 779--794
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