Almost additive multifractal analysis

Almost Additive Thermodynamic Formalism: Some Recent Developments

This is a survey on recent developments concerning a thermodynamic formalism for almost additive sequences of functions. While the nonadditive thermodynamic formalism applies to much more general sequences, at the present stage of the theory there are no general results concerning for example a variational principle for the topological pressure or the existence of equilibrium or Gibbs measures,...

On Additive Almost Continuous Functions under Cpa

We prove that the Covering Property Axiom CPA prism, which holds in the iterated perfect set model, implies that there exists an additive discontinuous almost continuous function f : R → R whose graph is of measure zero. We also show that, under CPA prism, there exists a Hamel basis H for which, E+(H), the set of all linear combinations of elements from H with positive rational coefficients, is...

Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments

We consider a family of stochastic processes built from infinite sums of independent positive random functions on R+. Each of these functions increases linearly between two consecutive negative jumps, with the jump points following a Poisson point process on R+. The motivation for studying these processes stems from the fact that they constitute simplified models for TCP traffic on the Internet...

Multifractal analysis for all

Multifractal formalism and analysis have been described many times (Lopes and Betrouni, 2009). There are several approaches to the implementation of multifractal analysis and there numerous ways to present these (Olsen, 1995; Wendt et al., 2009; Ihlen, 2012). Ihlen’s article, in the June 4th 2012 issue of Frontiers of Physiology, entitled “Introduction to multifractal detrended fluctuation anal...

Box-counting multifractal analysis.