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Teor. Veroyatnost. i Primenen., 1998, Volume 43, Issue 3, Pages 490–508 (Mi tvp1556)  

This article is cited in 4 scientific papers (total in 4 papers)

On the necessary conditions of normal convergence for martingales

A. G. Sholomitskii

Central Economics and Mathematics Institute, RAS

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.

DOI: https://doi.org/10.4213/tvp1556

Full text: PDF file (819 kB)

English version:
Theory of Probability and its Applications, 1999, 43:3, 434–448

Bibliographic databases:

Received: 06.03.1997

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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\yr 1998
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\pages 490--508
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\transl
\jour Theory Probab. Appl.
\yr 1999
\vol 43
\issue 3
\pages 434--448
\crossref{https://doi.org/10.1137/S0040585X97977021}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. M. Kruglov, “On the Necessity of the Lindeberg Condition for the Normal Convergence of Martingales”, Math. Notes, 70:1 (2001), 46–52  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. G. Sholomitskii, “On the necessary conditions of Poisson convergence for martingales”, Theory Probab. Appl., 49:4 (2005), 735–737  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Fiorina J., Hachem W., “On the asymptotic distribution of the correlation receiver output for time–hopped UWB signals”, IEEE Transactions on Signal Processing, 54:7 (2006), 2529–2545  crossref  zmath  adsnasa  isi  scopus
    4. Cheng Ts.-L. Yang Sh.-Y., “Stable Poisson Convergence for Integer-Valued Random Variables”, Taiwan. J. Math., 17:6 (2013), 1869–1885  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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