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On the asymptotic and invariantσ-algebras of random walks on locally compact groups
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  • Published: June 1995

On the asymptotic and invariantσ-algebras of random walks on locally compact groups

  • Wojciech Jaworski1 nAff2 

Probability Theory and Related Fields volume 101, pages 147–171 (1995)Cite this article

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  • 9 Citations

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Summary

Consider a random walk of law μ on a locally compact second countable groupG. Let the starting measure be equivalent to the Haar measure and denote byQ the corresponding Markov measure on the space of pathsG ∞. We study the relation between the spacesL ∞ (G ∞, ℬa,Q) andL ∞ (G ∞, ℬi,Q) where ℬa and ℬi stand for the asymptotic and invariant σ-algebras, respectively. We obtain a factorizationL ∞ (G ∞, ℬa,Q) ≊L ∞ (G ∞, ℬi,Q)⊗L ∞ (C) whereC is a cyclic group whose order (finite or infinite) coincides with the period of the Markov shift and is determined by the asymptotic behaviour of the convolution powersμ n.

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Author information

Author notes
  1. Wojciech Jaworski

    Present address: Department of Mathematics, Statistics, and Computing Science, Dalhousie University, B3H 3J5, Halifax, Nova Scotia, Canada

Authors and Affiliations

  1. Department of Mathematics, University of Ottawa, K1N 6N5, Ottawa, Ontario, Canada

    Wojciech Jaworski

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  1. Wojciech Jaworski
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Jaworski, W. On the asymptotic and invariantσ-algebras of random walks on locally compact groups. Probab. Th. Rel. Fields 101, 147–171 (1995). https://doi.org/10.1007/BF01375822

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  • Received: 05 March 1992

  • Revised: 22 June 1994

  • Issue Date: June 1995

  • DOI: https://doi.org/10.1007/BF01375822

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Mathematics Subject Classification

  • 60B15
  • 60J15
  • 60J50
  • 43A05
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