Probability Theory and Related Fields

, Volume 101, Issue 2, pp 147–171 | Cite as

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

  • Wojciech Jaworski


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 powersμn.

Mathematics Subject Classification

60B15 60J15 60J50 43A05 


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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Wojciech Jaworski
    • 1
  1. 1.Department of MathematicsUniversity of OttawaOttawaCanada

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