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Teor. Veroyatnost. i Primenen., 2016, Volume 61, Issue 4, Pages 659–685 (Mi tvp5082)  

This article is cited in 3 scientific papers (total in 3 papers)

Generalization and refinement of the integro-local Stone theorem for sums of random vectors

A. A. Borovkov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: The integro-local Stone theorem on the asymptotics of the probability that a sum of random vectors enters a small cube is (a) refined under additional moment and structural conditions; (b) generalized to a case of nonidentically distributed summands in the triangular array scheme; (c) the results of item (b) are refined under additional moment and structural conditions.

Keywords: integro-local Stone theorem, sums of random vectors, bound for the remainder term, triangular array scheme.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00220


DOI: https://doi.org/10.4213/tvp5082

Full text: PDF file (326 kB)
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English version:
Theory of Probability and its Applications, 2017, 61:4, 590–612

Bibliographic databases:

Received: 15.01.2016

Citation: A. A. Borovkov, “Generalization and refinement of the integro-local Stone theorem for sums of random vectors”, Teor. Veroyatnost. i Primenen., 61:4 (2016), 659–685; Theory Probab. Appl., 61:4 (2017), 590–612

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Borovkov, “Integro-local limit theorems for compound renewal processes”, Theory Probab. Appl., 62:2 (2018), 175–195  mathnet  crossref  crossref  mathscinet  isi  elib
    2. L. V. Rozovskii, “Integro-local CLT for sums of independent nonlattice random vectors”, Theory Probab. Appl., 64:1 (2019), 27–40  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. L. V. Rozovskii, “On integro-local CLT for sums of independent random vectors”, Theory Probab. Appl., 64:4 (2020), 564–578  mathnet  crossref  crossref  isi  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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