Unique Bernoulli g-measures
2012 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 14, no 5, 1599-1615 p.Article in journal (Refereed) Published
We improve and subsume the conditions of Johansson and O¨ berg  and Berbee 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  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.
Place, publisher, year, edition, pages
European Mathematical Society Publishing House, 2012. Vol. 14, no 5, 1599-1615 p.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-126899DOI: 10.4171/JEMS/342ISI: 000308126300009OAI: oai:DiVA.org:uu-126899DiVA: diva2:327596