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Teoriya Veroyatnostei i ee Primeneniya, 1998, Volume 43, Issue 3, Pages 490–508
DOI: https://doi.org/10.4213/tvp1556 (Mi tvp1556) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On the necessary conditions of normal convergence for martingales

A. G. Sholomitskii

Central Economics and Mathematics Institute, RAS
Full-text PDF (819 kB) Citations (5)
DOI: https://doi.org/10.4213/tvp1556
Abstract: The necessity of the Lindeberg condition for the normal convergence of sums of martingale differences is proved under some additional symmetry assumptions imposed on the summands. The invariance principle may not hold.
Keywords: martingales, conditional Lindeberg condition, limiting negligibility, conditional moments.
Received: 06.03.1997
English version:
Theory of Probability and its Applications, 1999, Volume 43, Issue 3, Pages 434–448
DOI: https://doi.org/10.1137/S0040585X97977021
Bibliographic databases:
Language: Russian
Citation: A. G. Sholomitskii, “On the necessary conditions of normal convergence for martingales”, Teor. Veroyatnost. i Primenen., 43:3 (1998), 490–508; Theory Probab. Appl., 43:3 (1999), 434–448
Citation in format AMSBIB
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\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 3
\pages 434--448
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  • https://doi.org/10.4213/tvp1556
  • https://www.mathnet.ru/eng/tvp/v43/i3/p490
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
     
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