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Teoriya Veroyatnostei i ee Primeneniya, 2003, Volume 48, Issue 4, Pages 701–719
DOI: https://doi.org/10.4213/tvp252
(Mi tvp252)
 

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

Abelian theorems, limit properties of conjugate distributions, and large deviations for sums of independent random vectors

A. Yu. Zaigraev, A. V. Nagaev

Nikolaus Copernicus University
References:
Abstract: A class of multidimensional absolutely continuous distributions is considered. Each distribution has a moment generating function, which is finite in a bounded convex set $S$ and generates a family of the so-called conjugate distributions. We focus our attention on the limit distributions for this family when the conjugate parameter tends to the boundary of $S$. As in the one-dimensional case, each limit distribution is obtained as a corollary of the Abel-type theorem. The results obtained are utilized for establishing a local limit theorem for large deviations of arbitrarily high order.
Keywords: Cramér's condition, deviation function, gamma-like distribution, large deviations of arbitrarily high order, local limit theorem, regular variation, support function.
Received: 04.04.2000
Revised: 23.01.2001
English version:
Theory of Probability and its Applications, 2004, Volume 48, Issue 4, Pages 664–680
DOI: https://doi.org/10.1137/S0040585X97980713
Bibliographic databases:
Language: Russian
Citation: A. Yu. Zaigraev, A. V. Nagaev, “Abelian theorems, limit properties of conjugate distributions, and large deviations for sums of independent random vectors”, Teor. Veroyatnost. i Primenen., 48:4 (2003), 701–719; Theory Probab. Appl., 48:4 (2004), 664–680
Citation in format AMSBIB
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\by A.~Yu.~Zaigraev, A.~V.~Nagaev
\paper Abelian theorems, limit properties of conjugate distributions,
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\issue 4
\pages 701--719
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\zmath{https://zbmath.org/?q=an:1059.60035}
\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 4
\pages 664--680
\crossref{https://doi.org/10.1137/S0040585X97980713}
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  • https://www.mathnet.ru/eng/tvp252
  • https://doi.org/10.4213/tvp252
  • https://www.mathnet.ru/eng/tvp/v48/i4/p701
  • 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
    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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