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Products of random varibles depending on a random walk

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Abstract

LetX=(X n ) n≥0 denote an irreducible random walk (“ergodic” in the sense of [7]) on a compact metrizable abelian groupG. In this paper we characterize completely the limit distributions of the productsY n =X 0...X n . In particular we find necessary and sufficient conditions forX and/orG to imply that the products are asymptotically equidistributed in the mean, i. e. {im171-1} holds for all open,m G -regular subsetsA ofG (m G : normalized Haar measure).—For example ifG is monothetic and connected or ifX is asymptotically equidistributed (not merely in the mean) then the products are asymptotically equidistributed in the mean.

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  1. Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-7400, Tübingen 1, Germany

    Manfred Wolff

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  1. Manfred Wolff
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Dedicated to Prof. Dr. L. Schmetterer on his 60th Birthday

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Wolff, M. Products of random varibles depending on a random walk. Monatshefte für Mathematik 88, 171–187 (1979). https://doi.org/10.1007/BF01319101

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