References of "Esser, Céline"      in Complete repository Arts & humanities   Archaeology   Art & art history   Classical & oriental studies   History   Languages & linguistics   Literature   Performing arts   Philosophy & ethics   Religion & theology   Multidisciplinary, general & others Business & economic sciences   Accounting & auditing   Production, distribution & supply chain management   Finance   General management & organizational theory   Human resources management   Management information systems   Marketing   Strategy & innovation   Quantitative methods in economics & management   General economics & history of economic thought   International economics   Macroeconomics & monetary economics   Microeconomics   Economic systems & public economics   Social economics   Special economic topics (health, labor, transportation…)   Multidisciplinary, general & others Engineering, computing & technology   Aerospace & aeronautics engineering   Architecture   Chemical engineering   Civil engineering   Computer science   Electrical & electronics engineering   Energy   Geological, petroleum & mining engineering   Materials science & engineering   Mechanical engineering   Multidisciplinary, general & others Human health sciences   Alternative medicine   Anesthesia & intensive care   Cardiovascular & respiratory systems   Dentistry & oral medicine   Dermatology   Endocrinology, metabolism & nutrition   Forensic medicine   Gastroenterology & hepatology   General & internal medicine   Geriatrics   Hematology   Immunology & infectious disease   Laboratory medicine & medical technology   Neurology   Oncology   Ophthalmology   Orthopedics, rehabilitation & sports medicine   Otolaryngology   Pediatrics   Pharmacy, pharmacology & toxicology   Psychiatry   Public health, health care sciences & services   Radiology, nuclear medicine & imaging   Reproductive medicine (gynecology, andrology, obstetrics)   Rheumatology   Surgery   Urology & nephrology   Multidisciplinary, general & others Law, criminology & political science   Civil law   Criminal law & procedure   Criminology   Economic & commercial law   European & international law   Judicial law   Metalaw, Roman law, history of law & comparative law   Political science, public administration & international relations   Public law   Social law   Tax law   Multidisciplinary, general & others Life sciences   Agriculture & agronomy   Anatomy (cytology, histology, embryology...) & physiology   Animal production & animal husbandry   Aquatic sciences & oceanology   Biochemistry, biophysics & molecular biology   Biotechnology   Entomology & pest control   Environmental sciences & ecology   Food science   Genetics & genetic processes   Microbiology   Phytobiology (plant sciences, forestry, mycology...)   Veterinary medicine & animal health   Zoology   Multidisciplinary, general & others Physical, chemical, mathematical & earth Sciences   Chemistry   Earth sciences & physical geography   Mathematics   Physics   Space science, astronomy & astrophysics   Multidisciplinary, general & others Social & behavioral sciences, psychology   Animal psychology, ethology & psychobiology   Anthropology   Communication & mass media   Education & instruction   Human geography & demography   Library & information sciences   Neurosciences & behavior   Regional & inter-regional studies   Social work & social policy   Sociology & social sciences   Social, industrial & organizational psychology   Theoretical & cognitive psychology   Treatment & clinical psychology   Multidisciplinary, general & others     Showing results 1 to 20 of 44 1 2 3     A new multifractional process with random exponentAyache, Antoine; Esser, Céline ; Hamonier, Julienin Risk and Decision Analysis (in press)A first type of Multifractional Process with Random Exponent (MPRE) was constructed several years ago by replacing in a wavelet series representation of Fractional Brownian Motion (FBM) the Hurst ... [more ▼]A first type of Multifractional Process with Random Exponent (MPRE) was constructed several years ago by replacing in a wavelet series representation of Fractional Brownian Motion (FBM) the Hurst parameter by a random variable depending on the time variable. In the present article, we propose another approach for constructing another type of MPRE. It consists in substituting to the Hurst parameter, in a stochastic integral representation of the high-frequency part of FBM, a random variable depending on the integration variable. The MPRE obtained in this way offers, among other things, the advantages to have a representation through classical Itô integral and to be less difficult to simulate than the first type of MPRE, previously introduced. Yet, the study of Hölder regularity of this new MPRE is a significantly more challenging problem than in the case of the previous one. Actually, it requires to develop a new methodology relying on an extensive use of the Haar basis. [less ▲] Divergence of wavelet series: A multifractal analysisEsser, Céline ; Jaffard, Stéphane in Advances in Mathematics (in press)We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs ... [more ▼]We show the relevance of a multifractal-type analysis for pointwise convergence and divergence properties of wavelet series: Depending on the sequence space which the wavelet coefficients sequence belongs to, we obtain deterministic upper bounds for the Hausdorff dimensions of the sets of points where a given rate of divergence occurs, and we show that these bounds are generically optimal, according to several notions of genericity. [less ▲]Detailed reference viewed: 18 (1 ULiège) Quelques questions autour des séries de FourierEsser, Céline Conference (2018, April 07)L'étude des séries de Fourier a motivé le développement de concepts importants de l'analyse au 19e siècle, avec notamment la théorie de l'intégration et la théorie des ensembles, et pose encore aujourd ... [more ▼]L'étude des séries de Fourier a motivé le développement de concepts importants de l'analyse au 19e siècle, avec notamment la théorie de l'intégration et la théorie des ensembles, et pose encore aujourd'hui de nombreuses questions. Dans cet exposé, nous présenterons quelques problèmes classiques liés aux séries de Fourier. En particulier, nous étudierons leur convergence et leur divergence, et nous nous pencherons sur les problèmes liés à l'unicité du développement. [less ▲] Results of genericity concerning ultradifferentiable classesEsser, Céline Scientific conference (2018, March 06)The aim of this talk is to give several results concerning the ''size'' (from different points of view) of sets defined using ultradifferentiable classes. More precisely, it is known that the set of ... [more ▼]The aim of this talk is to give several results concerning the ''size'' (from different points of view) of sets defined using ultradifferentiable classes. More precisely, it is known that the set of nowhere analytic functions is ''large'' in the space of smooth functions; We will first show how to extend these results to nowhere Gevrey functions. Then, we will study functions which are nowhere quasianalytic or nowhere in a given ultradifferentiable class. Finally, we will present some recent results concerning the size of the image of non-sujective Borel mappings. [less ▲] How far is the Borel map from being surjective in quasianalytic ultradifferentiable classes?,Esser, Céline ; Schindl, GerhardE-print/Working paper (2018)The Borel map $j^{\infty}$ takes germs at 0 of smooth functions to the sequence of iterated partial derivatives at 0. In the literature, it is well known that the restriction of $j^{\infty}$ to the germs ... [more ▼]The Borel map $j^{\infty}$ takes germs at 0 of smooth functions to the sequence of iterated partial derivatives at 0. In the literature, it is well known that the restriction of $j^{\infty}$ to the germs of quasianalytic ultradifferentiable classes which are strictly containing the real analytic functions can never be onto the corresponding sequence space. In this paper, we are interested in studying how large the image of $j^{\infty}$ is and we investigate the size and the structure of this image by using different approaches (Baire residuality, prevalence and lineability). We give an answer to this question in the very general setting of quasianalytic ultradifferentiable classes defined by weight matrices, which contains as particular cases the classes defined by a single weight sequence or by a weight function. [less ▲] An algorithm for computing non-concave multifractal spectra using the Sν spacesKleyntssens, Thomas ; Esser, Céline ; Nicolay, Samuel in Communications in Nonlinear Science & Numerical Simulation (2018), 56We present an implementation of a multifractal formalism based on the Sν spaces and show that it effectively gives the right Hölder spectrum in numerous cases. In particular, it allows to recover non ... [more ▼]We present an implementation of a multifractal formalism based on the Sν spaces and show that it effectively gives the right Hölder spectrum in numerous cases. In particular, it allows to recover non-concave spectra, where other multifractal formalisms only lead to the concave hull of the spectra. [less ▲]Detailed reference viewed: 48 (9 ULiège) A multifractal formalism for non-concave and non-increasing spectra: the leaders profile methodEsser, Céline ; Kleyntssens, Thomas ; Nicolay, Samuel in Applied & Computational Harmonic Analysis (2017), 43(2), 269-291We present an implementation of a multifractal formalism based on the types of histogram of wavelet leaders. This method yields non-concave spectra and is not limited to their increasing part. We show ... [more ▼]We present an implementation of a multifractal formalism based on the types of histogram of wavelet leaders. This method yields non-concave spectra and is not limited to their increasing part. We show both from the theoretical and from the applied points of view that this approach is more e cient than the wavelet-based multifractal formalisms previously introduced. [less ▲]Detailed reference viewed: 125 (40 ULiège) Lineability in multifractal analysisEsser, Céline ; Jaffard, Stéphane E-print/Working paper (2017)The multifractal behavior of generic functions belonging to H older, Sobolev or Besov spaces has been investigated by many authors, using the concepts of Baire residuality and of prevalence. This paper ... [more ▼]The multifractal behavior of generic functions belonging to H older, Sobolev or Besov spaces has been investigated by many authors, using the concepts of Baire residuality and of prevalence. This paper aims at obtaining the corresponding results in the framework supplied by the notion of lineability. Furthermore, we also study the question of algebrability, proving negative and positive results. [less ▲] Different possible behaviors of wavelet leaders of the Brownian motionAyache, Antoine; Esser, Céline ; Kleyntssens, Thomas E-print/Working paper (2017)The aim of this paper is to prove that wavelet leaders allow to get very fine properties of the trajectories of the Brownian motion: more precisely, we show that there exist (at least) three different ... [more ▼]The aim of this paper is to prove that wavelet leaders allow to get very fine properties of the trajectories of the Brownian motion: more precisely, we show that there exist (at least) three different behaviors for the size of wavelet leaders of the Brownian motion. Furthermore, they correspond to the three well-known behaviors of its oscillations, namely to be ordinary, rapid and slow. Some links between the oscillations and the size of wavelet leaders at a given point are also given. [less ▲]Detailed reference viewed: 18 (4 ULiège) Almost sure approximations in Hölder norms of a general stochastic process defined by a Young integralAyache, Antoine; Esser, Céline ; Qidi, PengE-print/Working paper (2017)We focus on a stochastic process $\{Y(t)\}_{t\in [0,v]}$ defined by a pathwise Young integral of a general form. Thanks to the Haar basis, we connect the classical method of approximation of $\{Y(t)\}_{t ... [more ▼]We focus on a stochastic process$\{Y(t)\}_{t\in [0,v]}$defined by a pathwise Young integral of a general form. Thanks to the Haar basis, we connect the classical method of approximation of$\{Y(t)\}_{t\in [0,v]}$through Euler scheme and Riemann-Stieltjes sums with a new approach consisting in the use of an appropriate series representation of$\{Y(t)\}_{t\in [0,v]}$. This representation is obtained through a general compactly supported orthonormal wavelet basis. An advantage offered by the new approach with respect to the classical one is that a better almost sure rate of convergence in H\"older norms can be derived, under a general Gaussian condition. Also, this improved rate turns out to be optimal in some situations; typically, when the integrator associated to$\{Y(t)\}_{t\in [0,v]}$is a fractional Brownian motion of an arbitrary Hurst parameter, and the integrand is a deterministic nowhere vanishing function with an invariant H\"older regularity large enough. [less ▲]Detailed reference viewed: 32 (1 ULiège) A useful result related with zeros of continuous compactly supported mother waveletsAyache, Antoine; Esser, Céline in International Journal of Wavelets, Multiresolution and Information Processing (2017), 15(5), 1750044In the last two decades, wavelet bases and associated methodologies have become quite important in many domains, such as signal and image processing, harmonic analysis, statistics, and so on. More ... [more ▼]In the last two decades, wavelet bases and associated methodologies have become quite important in many domains, such as signal and image processing, harmonic analysis, statistics, and so on. More recently, they also turn out to be quite useful in the probabilistic framework of stochastic processes, in which, among other things, they allow to obtain fine results concerning erratic sample paths behavior. The goal of our article is to derive a result, related with zeros of continuous compactly supported mother wavelets, which is useful in this probabilistic framework. More precisely, let$\psi$be any arbitrary such wavelet; we show that being given an arbitrary point$x_0\in\R$there always exists at least one integer$k_{x_0}\in\Z$such that$\psi(x_0-k_{x_0}) \neq 0\$. [less ▲]Detailed reference viewed: 31 (5 ULiège) Wavelet series representations for pathwise Young integralsEsser, Céline Conference (2016, October)Detailed reference viewed: 14 (2 ULiège) Propriétés multifractales de la divergence de séries d’ondelettesEsser, Céline Conference (2016, September 22)Dans cet exposé, nous nous intéressons à la divergence ponctuelle de séries d'ondelettes dans un espace de Besov donné. Nous obtenons une borne supérieure pour la dimension de Hausdorff de l'ensemble des ... [more ▼]Dans cet exposé, nous nous intéressons à la divergence ponctuelle de séries d'ondelettes dans un espace de Besov donné. Nous obtenons une borne supérieure pour la dimension de Hausdorff de l'ensemble des points ayant un taux de divergence donné, et nous montrons que cette borne est optimale en utilisant les notions de résidualité et de prévalence. [less ▲]Detailed reference viewed: 14 (2 ULiège) Multifractal analysis of the divergence of wavelet seriesEsser, Céline Conference (2016, June 07)In this talk, we study pointwise divergence properties of wavelet expansions of functions in a given Besov space. We obtain deterministic upper bounds for the Hausdorff dimensions of the sets of points ... [more ▼]In this talk, we study pointwise divergence properties of wavelet expansions of functions in a given Besov space. We obtain deterministic upper bounds for the Hausdorff dimensions of the sets of points where a given rate of divergence is observed, and we show that these bounds are generically (in the sense of Baire's categories) optimal. This gives a complement to the works done by F. Bayart and Y. Heurteaux in the case of Fourier series and by J.M. Aubry. [less ▲]Detailed reference viewed: 22 (4 ULiège) Représentation d'intégrales stochastiques via la base de HaarEsser, Céline Conference (2016, May 24)Detailed reference viewed: 18 (2 ULiège) Analyse multifractale de la vitesse de divergence de séries d'ondelettesEsser, Céline Scientific conference (2016, May 13)Detailed reference viewed: 7 (0 ULiège) Large deviation spectra based on wavelet leadersBastin, Françoise ; Esser, Céline ; Jaffard, Stéphane in Revista Matemática Iberoamericana (2016), 32(3), 859-890We introduce a new multifractal formalism, based on distributions of wavelet leaders, which allows to detect non-concave and decreasing multifractal spectra, and we investigate the properties of the ... [more ▼]We introduce a new multifractal formalism, based on distributions of wavelet leaders, which allows to detect non-concave and decreasing multifractal spectra, and we investigate the properties of the associated function spaces. [less ▲]Detailed reference viewed: 160 (27 ULiège) Estimation de spectres de singularités par des méthodes de grandes déviations basées sur les ondelettesEsser, Céline Scientific conference (2015, December 02)La régularité d'un signal en un point peut être caractérisée par son exposant de Hölder. Une description synthétique de la répartition des différents exposants de Hölder d'un signal est fournie par son ... [more ▼]La régularité d'un signal en un point peut être caractérisée par son exposant de Hölder. Une description synthétique de la répartition des différents exposants de Hölder d'un signal est fournie par son spectre de singularités. Plusieurs méthodes basées sur la décomposition en ondelettes ont été proposées pour estimer le spectre de singularités d'un signal; elles reposent sur une caractérisation de l'exposant de Hölder par les coefficients d'ondelettes. Dans cet exposé, nous présentons une nouvelle méthode reposant sur des estimations de grandes déviations basées sur les coefficients d'ondelettes et montrons son efficacité sur plusieurs exemples déterministes ou non. [less ▲]Detailed reference viewed: 13 (4 ULiège) Estimation de spectres de singularités par des techniques de grandes déviations basées sur les ondelettesEsser, Céline Conference (2015, November 26)La régularité en un point d'une fonction peut être caractérisée par son exposant de Hölder. Si la fonction est très irrégulière, celui-ci peut varier fortement d'un point à l'autre. Dans ce cas, il est ... [more ▼]La régularité en un point d'une fonction peut être caractérisée par son exposant de Hölder. Si la fonction est très irrégulière, celui-ci peut varier fortement d'un point à l'autre. Dans ce cas, il est naturel d'étudier la distribution des exposants de Hölder: cette information est donnée par le spectre de singularités de la fonction. En général, ce spectre est assez difficile à calculer et on utilise des méthodes pour l'estimer. Plusieurs méthodes basées sur la décomposition en ondelettes ont été proposées ; elles reposent sur une caractérisation de l'exposant de Hölder par les coefficients d'ondelettes. Dans cet exposé, nous introduisons une nouvelle technique reposant sur des estimations de grandes déviations basées sur les coefficients d'ondelettes et montrons son efficacité sur plusieurs exemples [less ▲]Detailed reference viewed: 25 (1 ULiège) Analyse multifractale de la divergence de séries d'ondelettesEsser, Céline Scientific conference (2015, November 06)Dans cet exposé, nous étudions la divergence ponctuelle de séries d'ondelettes dans un espace de Besov. Nous obtenons une borne supérieure pour la dimension de Hausdorff de l'ensemble des points ayant un ... [more ▼]Dans cet exposé, nous étudions la divergence ponctuelle de séries d'ondelettes dans un espace de Besov. Nous obtenons une borne supérieure pour la dimension de Hausdorff de l'ensemble des points ayant un taux de divergence donné, et nous montrons que cette borne est optimale en utilisant les notions de résidualité et de prévalence. Il s'agit d'un travail en collaboration avec S. Jaffard. [less ▲]Detailed reference viewed: 4 (0 ULiège) 1 2 3