Geodesic
Stability problems in Cram\'er-type characterization in case of I.I.D. Summands
Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 701-723

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The stability property in Cramér’s characterization of the normal law is considered in the case of identically distributed summands. As opposite results, instability is shown with respect to strong distances including the entropic distance to normality (addressing a question of M. Kac).
Keywords: Cramér’s theorem; Cramér’s characterization of the normal law; stability problems. 
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     author = {S. G. Bobkov and G. P. Chistyakov and F. G\"otze},
     title = {Stability problems in {Cram\'er-type} characterization in case of {I.I.D.} {Summands}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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S. G. Bobkov; G. P. Chistyakov; F. Götze. Stability problems in Cram\'er-type characterization in case of I.I.D. Summands. Teoriâ veroâtnostej i ee primeneniâ, Tome 57 (2012) no. 4, pp. 701-723. http://geodesic.mathdoc.fr/item/TVP_2012_57_4_a4/