Geodesic
On the central limit Newman theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 382-390

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We construct an example of a strictly stationary associated random sequence which does not satisfy the central limit theorem and whose the partial sums' variance grows in a defined regular way. This result generalizes the well-known example of N. Herrndorf and shows the optimality of conditions in the classical Newman's theorem.
Keywords: associated random variables, stationarity, central limit theorem, slowly varying functions. 
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     author = {A. P. Shashkin},
     title = {On the central limit {Newman} theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {382--390},
     publisher = {mathdoc},
     volume = {50},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a12/}
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A. P. Shashkin. On the central limit Newman theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 382-390. http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a12/