Heyde's characterization theorem for some locally compact Abelian groups
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 3, pp. 499-517
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By Heyde's theorem, the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of $n$ independent random variables with the other fixed. When $n=2$ we prove analogues of this theorem in the case when independent random variables take values in a locally compact Abelian group $X$ and coefficients of the linear forms are topological automorphisms of $X$.
Keywords:
locally compact Abelian group, Gaussian distribution, conditional distribution.
@article{TVP_2017_62_3_a3,
author = {G. M. Feldman},
title = {Heyde's characterization theorem for some locally compact {Abelian} groups},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {499--517},
publisher = {mathdoc},
volume = {62},
number = {3},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_3_a3/}
}
G. M. Feldman. Heyde's characterization theorem for some locally compact Abelian groups. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 3, pp. 499-517. http://geodesic.mathdoc.fr/item/TVP_2017_62_3_a3/