Geodesic
On the necessary conditions of normal convergence for martingales
Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 3, pp. 490-508

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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.
Mots-clés : martingales, conditional moments.
Keywords: conditional Lindeberg condition, limiting negligibility 
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     author = {A. G. Sholomitskii},
     title = {On the necessary conditions of normal convergence for martingales},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {490--508},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1998_43_3_a4/}
}
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A. G. Sholomitskii. On the necessary conditions of normal convergence for martingales. Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 3, pp. 490-508. http://geodesic.mathdoc.fr/item/TVP_1998_43_3_a4/