We define an asymptotically normal wavelet-based strongly consistent estimator for the Hurst parameter of any Hermite processes. This estimator is obtained by considering a modified wavelet variation in which coefficients are wisely chosen to be, up to negligeable remainders, independent. We use Stein-Malliavin calculus to prove that this wavelet v...
In this talk, I first present the general framework of Cantor real numeration system, which allow us to represent all non-negative real numbers via a bi-infinite sequence of real bases by using a greedy algorithm. These systems appear naturally in the framework of positional numeration systems for representing integers, and they generalize the exte...
In this talk, I first present the general framework of Cantor real numeration system, which allow us to represent all non-negative real numbers via a bi-infinite sequence of real bases by using a greedy algorithm. These systems appear naturally in the framework of positional numeration systems for representing integers, and they generalize the exte...
This paper presents a new model of textures, obtained as realizations of a new class of fractional Brownian fields. These fields, called weighted tensorized fractional Brownian fields, are obtained by a relaxation of the tensor-product structure that appears in the definition of fractional Brownian sheets. Statistical properties such as self-simila...
A classical result states that, when applying a non-erasing morphism to a word, the factor complexity of the image is bounded by the initial factor complexity multiplied by a constant depending on the morphism. However, when looking at the proof, one easily sees that this can be vastly improved. This is the object of this talk in which we exhibit a...
editorial reviewed
peer reviewed / We generalize here the notion of interpolation space of given exponent by replacing this exponent with Boyd functions. In particular, this approach leads to the usual interpolation method with a function parameter. We present some results in this general setting. Some are well-known, others not so well.
peer reviewed / In this paper, we look at the local and global solutions of the Fréchet functional equation for connected Lie groups. In particular, we give a characterization of these solutions using the lower central series, providing a notion of polynomial for such groups.
