ISSN:
1432-2064
Keywords:
60B15
;
60J15
;
60J50
;
43A05
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 ∞, ℬ a ,Q) andL ∞ (G ∞, ℬ i ,Q) where ℬ a and ℬ i stand for the asymptotic and invariant σ-algebras, respectively. We obtain a factorizationL ∞ (G ∞, ℬ a ,Q) ≊L ∞ (G ∞, ℬ i ,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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01375822
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