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pro vyhledávání: '"Loosveldt"'
We investigate a new class of self-similar fractional Brownian fields, called Weighted Tensorized Fractional Brownian Fields (WTFBS). These fields, introduced in the companion paper \cite{ELLV}, generalize the well-known fractional Brownian sheet (FB
Externí odkaz:
http://arxiv.org/abs/2412.03366
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
Externí odkaz:
http://arxiv.org/abs/2406.03313
Autor:
Loosveldt, Laurent, Tudor, Ciprian A.
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
Externí odkaz:
http://arxiv.org/abs/2403.05140
Wavelet-type random series representations of the well-known Fractional Brownian Motion (FBM) and many other related stochastic processes and fields have started to be introduced since more than two decades. Such representations provide natural frame
Externí odkaz:
http://arxiv.org/abs/2303.05320
Autor:
Loosveldt, Laurent
We define multifractional Hermite processes which generalize and extend both multifractional Brownian motion and Hermite processes. It is done by substituting the Hurst parameter in the definition of Hermite processes as a multiple Wiener-It\^o integ
Externí odkaz:
http://arxiv.org/abs/2303.04680
Autor:
Esser, Céline, Loosveldt, Laurent
We study the pointwise regularity of the Multifractional Brownian Motion and in particular, we get the existence of slow points. It shows that a non self-similar process can still enjoy this property. We also consider various extensions of our result
Externí odkaz:
http://arxiv.org/abs/2302.06422
Autor:
Daw, Lara, Loosveldt, Laurent
We prove that we can identify three types of pointwise behaviour in the regularity of the (generalized) Rosenblatt process. This extends to a non Gaussian setting previous results known for the (fractional) Brownian motion. On this purpose, fine boun
Externí odkaz:
http://arxiv.org/abs/2203.08487
Autor:
Esser, Céline, Loosveldt, Laurent
We study the H\"olderian regularity of Gaussian wavelets series and show that they display, almost surely, three types of points: slow, ordinary and rapid. In particular, this fact holds for the Fractional Brownian Motion. We also show that this prop
Externí odkaz:
http://arxiv.org/abs/2203.05472
We consider the space of real-valued continuously differentiable functions on a compact subset of a euclidean space. We characterize the completeness of this space and prove that the space of restrictions of continuously differentiable functions on t
Externí odkaz:
http://arxiv.org/abs/2003.09681
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