Geodesic
On one property of symmetrized distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 1, pp. 68-71

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The present paper studies the connection between the local limit theorem for lattice random variables and the corresponding symmetrized random variables. An example is constructed to show that the local limit theorem holds for some sequence of symmetrized random variables, but fails to hold for the original random variables.
Keywords: local limit theorem for lattice random variables, local limit theorem for symmetrized random variables. 
@article{TVP_2017_62_1_a4,
     author = {N. G. Gamkrelidze},
     title = {On one property of symmetrized distributions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {68--71},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_1_a4/}
}
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N. G. Gamkrelidze. On one property of symmetrized distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 1, pp. 68-71. http://geodesic.mathdoc.fr/item/TVP_2017_62_1_a4/