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Unique Bernoulli g-...
Unique Bernoulli g-measures
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- Johansson, Anders, 1960- (författare)
- Högskolan i Gävle,Uppsala universitet,Analys och tillämpad matematik,Matematik,Uppsala University, Department of Mathematics
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- Öberg, Anders, 1968- (författare)
- Uppsala universitet,Analys och tillämpad matematik,Uppsala University, Department of Mathematics
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- Pollicott, Mark, 1959- (författare)
- University of Warwick, Coventry, England,University of Warwick, Mathematics Institute
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(creator_code:org_t)
- European Mathematical Society Publishing House, 2012
- 2012
- Engelska.
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society Publishing House. - 1435-9855 .- 1435-9863. ; 14:5, s. 1599-1615
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Abstract
Ämnesord
Stäng
- We improve and subsume the conditions of Johansson and O¨ berg [18] and Berbee [2]for uniqueness of a g-measure, i.e., a stationary distribution for chains with complete connections.In addition, we prove that these unique g-measures have Bernoulli natural extensions. In particular,we obtain a unique g-measure that has the Bernoulli property for the full shift on finitely manystates under any one of the following additional assumptions.(1)P1n=1(varn log g)2 < 1,(2) For any fixed ✏ > 0,P1n=1 e−(1/2+✏)(var1 log g+···+varn log g) = 1,(3) varn log g = o(1/pn) as n!1.That the measure is Bernoulli in the case of (1) is new. In (2) we have an improved version ofBerbee’s [2] condition (concerning uniqueness and Bernoullicity), allowing the variations of log gto be essentially twice as large. Finally, (3) is an example that our main result is new both foruniqueness and for the Bernoulli property.We also conclude that we have convergence in the Wasserstein metric of the iterates of theadjoint transfer operator to the g-measure.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
Nyckelord
- Mathematical analysis
- Analys
- Mathematics
- Matematik
- Bernoulli measure
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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