A new class of random multiplicative and statistically self-similar measures is de ned on R. It is the limit of measure-valued martingales constructed by multiplying random functions attached to theâ€¦ (More)

Let {xn}nâˆˆN be a sequence of [0, 1]d, {Î»n}nâˆˆN a sequence of positive real numbers converging to 0, and Î´ > 1. The classical ubiquity results are concerned with the computation of the Hausdorffâ€¦ (More)

Let {xn}nâˆˆN be a sequence in [0, 1]d, {Î»n}nâˆˆN a sequence of positive real numbers converging to 0, and Î´ > 1. The classical ubiquity results are concerned with the computation of the Hausdorffâ€¦ (More)

This paper investigates new properties concerning the multifrac-tal structure of a class of statistically self-similar measures. These measures include the well-known Mandelbrot multiplicativeâ€¦ (More)

We construct a non-decreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the singularity spectrum of this process, which turns outâ€¦ (More)

We are interested in two properties of real numbers: the first one is the property of being well-approximated by some dense family of real numbers {xn}nâ‰¥1, such as rational numbers and more generallyâ€¦ (More)

In this note, we make explicit the limit law of the renormalized supercritical branching random walk, giving credit to a conjecture formulated in [5] for a continuous analogue of the branching randomâ€¦ (More)

We consider a class of Gibbs measures on self-affine Sierpinski carpets and perform the multifractal analysis of its elements. These deterministic measures are Gibbs measures associated with bundleâ€¦ (More)