On the Heyde Theorem for Finite Abelian Groups

G. M. Feldman
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G. M. Feldman: Institute for Low Temperature Physics and Engineering

Journal of Theoretical Probability, 2004, vol. 17, issue 4, 929-941

Abstract: Abstract It is well-known Heyde's characterization theorem for the Gaussian distribution on the real line: if ξ j are independent random variables, α j , β j are nonzero constants such that β i α ±β j α−1 j ≠ 0 for all i≠ j and the conditional distribution of L 2=β1 ξ1 + ··· + β n ξ n given L 1=α1 ξ1 + ··· +α n ξ n is symmetric, then all random variables ξ j are Gaussian. We prove some analogs of this theorem, assuming that independent random variables take on values in a finite Abelian group X and the coefficients α j ,β j are automorphisms of X.

Keywords: Characterization of probability distributions; idempotent distributions; finite Abelian groups (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/s10959-004-0583-0

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