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Limit theorems for convolutions of probabilities on non abelian semigroups

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Abstract

Let S be a locally compact semigroup. We study the sequence (λn) of the convolution powers of a probability measure λ on S and their shifts by a probability measure η on S. We shall give sufficient conditions for lim ‖λn−η*λn‖ = 0 (where ‖.‖ denotes the norm). In particular we consider the case the η is a point measure and we study the subsemigroup LO(λ) = {x ∈ S : lim ‖λn−δX*λn‖ = 0}. We shall give necessary and sufficient conditions for Lo(λ)=S. In this case we want to treat the problem of the convergence of the sequence (λn).

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  1. Institut für Mathematik, Universität Salzburg, Hellbrunnerstraße 34, A-5020, Salzburg, Austria

    Franz Kinzl

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  1. Franz Kinzl
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Kinzl, F. Limit theorems for convolutions of probabilities on non abelian semigroups. Semigroup Forum 38, 105–118 (1989). https://doi.org/10.1007/BF02573222

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  • DOI: https://doi.org/10.1007/BF02573222

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