References of "Kreit, Damien"
     in
Bookmark and Share    
Full Text
See detailOn Generalized Hölder-Zygmund Spaces
Kreit, Damien ULg

Doctoral thesis (2016)

To study the regularity of functions, many functional spaces have been introduced during the 20th century. Among them, let us mention the Hölder-Zygmund spaces \Lambda^{\alpha}(\R^{d}) and the Besov ... [more ▼]

To study the regularity of functions, many functional spaces have been introduced during the 20th century. Among them, let us mention the Hölder-Zygmund spaces \Lambda^{\alpha}(\R^{d}) and the Besov spaces B_{p,q}^{\alpha}(\R^{d}) where \alpha>0 somehow indicates the regularity of their elements (p,q\in ]0,+\infty]). The Hölder-Zygmund spaces are particular cases of Besov spaces in the sense that \Lambda^{\alpha}(\R^{d})=B_{\infty,\infty}^{\alpha}(\R^{d}). A generalization of Besov spaces has been introduced in the middle of the seventies and is still studied nowadays. This new type of space allows a deepest study of the regularity of functions. In this thesis, we start from this generalization in order to introduce a generalization of Hölder-Zygmund spaces. The first aim of this thesis is to show that most classical properties of Hölder-Zygmund spaces can be transposed to their generalized version. Among others, a complete characterization of these spaces in terms of wavelet coefficients is proved, which opens their use in the context of the signal analysis. The second aim of this thesis is to introduce a generalized version of the pointwise Hölder spaces similarly to their global version. We then show that most properties of the global spaces can be transposed to their generalized pointwise version. Finally, we study the regularity of some financial stochastic processes. [less ▲]

Detailed reference viewed: 19 (5 ULg)
Full Text
See detailSome characterizations about Generalized Hölder-Zygmund Spaces Λ_{σ,N}^{α}(R^d)
Kreit, Damien ULg; Nicolay, Samuel ULg

E-print/Working paper (2016)

Generalized Hölder-Zygmund spaces $\Lambda_{\sigma, N}^{\alpha}(\R^{d})$ were recently introduced and are based on a generalization of Besov spaces. Under some conditions, generalized Hölder-Zygmund and ... [more ▼]

Generalized Hölder-Zygmund spaces $\Lambda_{\sigma, N}^{\alpha}(\R^{d})$ were recently introduced and are based on a generalization of Besov spaces. Under some conditions, generalized Hölder-Zygmund and Besov spaces are equal. It has been proved that most properties of classical Hölder-Zygmund spaces are held for spaces $\Lambda^{\sigma,\alpha}(\R^{d})$, which constitute a particular case of spaces $\Lambda_{\sigma, N}^{\alpha}(\R^{d})$ with $N_{j}=2^{j}$. The goal of the present document is to prove that most of these properties are kept for $\Lambda_{\sigma, N}^{\alpha}(\R^{d})$ spaces. [less ▲]

Detailed reference viewed: 11 (1 ULg)
Full Text
See detailOn generalized Hölder-Zygmund spaces
Kreit, Damien ULg; Nicolay, Samuel ULg

Poster (2013, October 29)

The Hölder spaces provide a natural way for measuring the smoothness of a function. These spaces appear in different areas such as approximation theory and multifractal analysis. The purpose of this ... [more ▼]

The Hölder spaces provide a natural way for measuring the smoothness of a function. These spaces appear in different areas such as approximation theory and multifractal analysis. The purpose of this poster is to present a generalization of such spaces as well as some recent results about their characterizations. These spaces are a particular case of a generalization of Besov Spaces who have recently been extensively studied. [less ▲]

Detailed reference viewed: 44 (6 ULg)
Full Text
See detailCopules pour processus stochastiques financiers - Etude de la dépendance entre risque action et risque taux d'intérêt
Kreit, Damien ULg

Master's dissertation (2013)

Ce mémoire a pour objectif d'introduire le lecteur au concept de copules, à leur interprétation et à leur utilisation en pratique. Une application de la théorie des copules à l'étude de la dépendance ... [more ▼]

Ce mémoire a pour objectif d'introduire le lecteur au concept de copules, à leur interprétation et à leur utilisation en pratique. Une application de la théorie des copules à l'étude de la dépendance entre risque action et risque de taux d'intérêt est ensuite développée et illustrée. [less ▲]

Detailed reference viewed: 17 (1 ULg)
Full Text
Peer Reviewed
See detailCharacterizations of the elements of generalized Hölder-Zygmund spaces by means of their representation
Kreit, Damien ULg; Nicolay, Samuel ULg

in Journal of Approximation Theory (2013), 172

We give three characterizations of the elements of generalized Hölder-Zygmund spaces. The first one, based on the Littlewood-Paley decomposition is already known, but the proof given here is much simpler ... [more ▼]

We give three characterizations of the elements of generalized Hölder-Zygmund spaces. The first one, based on the Littlewood-Paley decomposition is already known, but the proof given here is much simpler. The second one, based on the wavelet decompositions generalizes a result obtained by Jaffard and Meyer. The third one uses generalized interpolation spaces. These results naturally extend the ones holding for the classical Hölder-Zygmund spaces. The manuscript has been accepted for publication in Journal of Approximation Theory. [less ▲]

Detailed reference viewed: 72 (19 ULg)
Full Text
Peer Reviewed
See detailSome characterizations of generalized Hölder spaces
Kreit, Damien ULg; Nicolay, Samuel ULg

in Mathematische Nachrichten (2012), 285(17-18), 2157-2172

Nous démontrons dans ce papier que les propriétés classiques des espaces de Hölder sont conservées pour les espaces de Hölder généralisés en terme de suite admissible. Nous donnons en particulier des ... [more ▼]

Nous démontrons dans ce papier que les propriétés classiques des espaces de Hölder sont conservées pour les espaces de Hölder généralisés en terme de suite admissible. Nous donnons en particulier des définitions équivalentes de ces espaces ainsi que des conditions d'emboitement de tels espaces. [less ▲]

Detailed reference viewed: 154 (47 ULg)
Full Text
See detailQuelques caractérisations des espaces de Hölder généralisés
Kreit, Damien ULg

Conference (2011, November 14)

Detailed reference viewed: 26 (4 ULg)
Full Text
See detailSur les espaces de Hölder ponctuels généralisés
Kreit, Damien ULg

Conference (2011, September 06)

We study a generalization of the well-known pointwise Hölder spaces. This generalization is based on another generalization of the (global) Hölder spaces (that we already studied and exposed on another ... [more ▼]

We study a generalization of the well-known pointwise Hölder spaces. This generalization is based on another generalization of the (global) Hölder spaces (that we already studied and exposed on another seminar). We show three main characterizations of these spaces, such as a characterization by the decay of the wavelet coefficients of their elements. [less ▲]

Detailed reference viewed: 34 (11 ULg)
Full Text
See detailOn generalized Hölder spaces
Kreit, Damien ULg; Nicolay, Samuel ULg

Poster (2011, June)

The Hölder spaces provide a natural way for measuring the smoothness of a function. These spaces appear in different areas such as approximation theory and multifractal analysis and lead to natural ... [more ▼]

The Hölder spaces provide a natural way for measuring the smoothness of a function. These spaces appear in different areas such as approximation theory and multifractal analysis and lead to natural definitions of the notion of fractal function; for example a function belonging to $C^\alpha$ with $\alpha\in (0,1)$ typically has a fractal graph. The purpose of this poster is to present a generalization of such spaces as well as some recent results about their characterizations. [less ▲]

Detailed reference viewed: 126 (20 ULg)
See detailSur l'équation fonctionnelle de Cauchy généralisée
Kreit, Damien ULg

Conference (2011, April 13)

Detailed reference viewed: 50 (12 ULg)
Full Text
See detailOn generalized Hölder spaces
Kreit, Damien ULg

Conference (2011, January 21)

Detailed reference viewed: 15 (4 ULg)
Full Text
See detailSome results about prevalence and strongly monoHölder functions
Kreit, Damien ULg

Poster (2010, September 13)

Detailed reference viewed: 13 (6 ULg)