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Teoriya Veroyatnostei i ee Primeneniya, 2018, Volume 63, Issue 4, Pages 779–794
DOI: https://doi.org/10.4213/tvp5149
(Mi tvp5149)
 

This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (518 kB) Citations (2)
References:
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 $M_t = \max_{i\in\{1,2,\dots,N_t\}} e^{tX_i}$, and the $l_t$ norm $R_t=S_t^{1/t}$, when $N_t\to\infty$ as $t\to\infty$ and $X_1,X_2,\dots$ 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
This research was supported by the Russian Science Foundation (grant 17-11-01098).
Received: 11.07.2017
Accepted: 05.04.2018
English version:
Theory of Probability and its Applications, 2019, Volume 63, Issue 4, Pages 634–647
DOI: https://doi.org/10.1137/S0040585X97T989295
Bibliographic databases:
Document Type: Article
Language: Russian
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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  • https://www.mathnet.ru/eng/tvp5149
  • https://doi.org/10.4213/tvp5149
  • https://www.mathnet.ru/eng/tvp/v63/i4/p779
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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