On measures driven by Markov chains

Yanick Heurteaux (1) , Andrzej Stos (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Mots clés: Multifractal formalism; Cantor sets; Hausdorff dimension; Markov chains

Domaines: Analyse classique [math.CA]; Géométrie métrique [math.MG]

Yanick Heurteaux, Andrzej Stos. On measures driven by Markov chains. 2013. ⟨hal-00880320⟩