This article is cited in 6 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.

Received: 06.03.1997

DOI: 10.4213/tvp1556

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

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