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Conformal measures and density estimation

Denker M., Facca T.

Probability and Mathematical Statistics

2011

Vol. 31, Fasc. 1

161--174

The notion of conformal measures or densities goes back to Patterson’s work [8]. By a theorem of Milnor and Thurston [7] a piecewise monotone and continuous map of the interval is semiconjugate to one with constant slopes. The semiconjugacies can be defined by distribution functions of conformal measures as shown in [2]. In this note we show that for some transformations the conjugacies are estimable functions and can be used to improve estimation procedures, in particular density estimations.

On the topological entropy of green interval maps

Bobok J.

Journal of Applied Analysis

2001

Vol. 7, nr 1

107-112

We investigate the topological entropy of a green interval map. Defining the complexity we estimate from above the topological entropy of a green interval map with a given complexity. The main result of the paper — stated in Theorem 0.2 — should be regarded as a completion of results of [4].