Abstract
We study measures on \([0,1]\) which are driven by a finite Markov chain and which generalize the famous Bernoulli products.We propose a hands-on approach to determine the structure function \(\tau \) and to prove that the multifractal formalism is satisfied. Formulas for the dimension of the measures and for the Hausdorff dimension of their supports are also provided. Finally, we identify the measures with maximal dimension.
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We would like to thank the anonymous Referees for their insightful comments that led to improvement of the paper.
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Heurteaux, Y., Stos, A. On Measures Driven by Markov Chains. J Stat Phys 157, 1046–1061 (2014). https://doi.org/10.1007/s10955-014-1104-x
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DOI: https://doi.org/10.1007/s10955-014-1104-x