Document Zbl 0639.60013

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Stability with respect to a group of actions, of probability laws defined on a finite Abelian group. (English. Russian original) Zbl 0639.60013

Theory Probab. Math. Stat. 33, 97-102 (1986); translation from Teor. Veroyatn. Mat. Stat. 33, 86-92 (1985).

Summary: Probability laws defined on a finite Abelian group and stable with respect to some group of actions are studied. It is shown that the probability law f(x) of a distribution is stable with respect to a group G if and only if the support B of the law f(x) satisfies the following conditions:
a) gB is a coset with respect to some subgroup of the group A for any g in G; b) GB is a subgroup of A.

MSC:

60B15	Probability measures on groups or semigroups, Fourier transforms, factorization
60E07	Infinitely divisible distributions; stable distributions

Keywords:

finite Abelian group; certain limit regularities; stable with respect to some group of actions

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