11 
Multiscale Total Variation Estimators for Regression and Inverse ProblemsÁlamo, Miguel del 24 May 2019 (has links)
No description available.

12 
Cohomologia e propriedades estocásticas de transformações expansoras e observáveis lipschitzianos / Cohomology and stochastics properties of expanding maps and lipschitzians observablesLima, Amanda de 20 March 2007 (has links)
Provamos o Teorema do Limite Central para transformações expansoras por pedaços em um intervalo e observáveis com variação limitada. Utilizamos a abordagem desenvolvida por R. RousseauEgele, como apresentada por A. Broise. O método da demonstração se baseia no estudo de pertubações do operador de transferência de RuellePerronFrobenius. Uma contribuição original é dada no último capítulo, onde provamos que, para transformações markovianas expansoras, todos os observáveis não constantes, contínuos e com variação limitada não são infinitamente cohomólogos à zero, generalizando um resultado de Bamón, RiveraLetelier, Urzúa and Kiwi para observáveis lipschitzianos e transformações \'z POT. n\' . A demonstração se baseia na teoria dos operadores de RuellePerronFrobenius desenvolvida nos capítulos anteriores / We prove the Central Limit Theorem for piecewise expanding interval transformations and observables with bounded variation, using the approach of J.RousseauEgele as described by A. Broise. This approach makes use of pertubations of the socalled RuellePerronFrobenius transfer operator. An original contribution is given in the last chapter, where we prove that for Markovian expanding interval maps all observables which are non constant, continuous and have bounded variation are not infinitely cohomologous with zero, generalizing a result by Bamón, RiveraLetelier, Urzúa and Kiwi for Lipschitzian observables and the transformations \'z POT. n\' . Our demosntration uses the theory of RuellePerronFrobenius operators developed in the previos chapters

13 
Functions of Generalized Bounded VariationLind, Martin January 2013 (has links)
This thesis is devoted to the study of different generalizations of the classical conception of a function of bounded variation. First, we study the functions of bounded pvariation introduced by Wiener in 1924. We obtain estimates of the total pvariation (1<p<∞) and other related functionals for a periodic function f in Lp([0,1]) in terms of its Lpmodulus of continuity ω(f;δ)p. These estimates are sharp for any rate of decay of ω(f;δ)p. Moreover, the constant coefficients in them depend on parameters in an optimal way. Inspired by these results, we consider the relationship between the Riesz type generalized variation vp,α(f) (1<p<∞, 0≤α≤11/p) and the modulus of pcontinuity ω11/p(f;δ). These functionals generate scales of spaces that connect the space of functions of bounded pvariation and the Sobolev space Wp1. We prove sharp estimates of vp,α(f) in terms of ω11/p(f;δ). In the same direction, we study relations between moduli of pcontinuity and qcontinuity for 1<p<q<∞. We prove an inequality that estimates ω11/p(f;δ) in terms of ω11/q(f;δ). The inequality is sharp for any order of decay of ω11/q(f;δ). Next, we study another generalization of bounded variation: the socalled bounded Λvariation, introduced by Waterman in 1972. We investigate relations between the space ΛBV of functions of bounded Λvariation, and classes of functions defined via integral smoothness properties. In particular, we obtain the necessary and sufficient condition for the embedding of the class Lip(α;p) into ΛBV. This solves a problem of Wang (2009). We consider also functions of two variables. Applying our onedimensional result, we obtain sharp estimates of the HardyVitali type pvariation of a bivariate function in terms of its mixed modulus of continuity in Lp([0,1]2). Further, we investigate Fubinitype properties of the space Hp(2) of functions of bounded HardyVitali pvariation. This leads us to consider the symmetric mixed norm space Vp[Vp]sym of functions of bounded iterated pvariation. For p>1, we prove that Hp(2) is not embedded into Vp[Vp]sym, and that Vp[Vp]sym is not embedded into Hp(2). In other words, Fubinitype properties completely fail in the class of functions of bounded HardyVitali type pvariation for p>1. / Baksidestext The classical concept of the total variation of a function has been extended in several directions. Such extensions find many applications in different areas of mathematics. Consequently, the study of notions of generalized bounded variation forms an important direction in the field of mathematical analysis. This thesis is devoted to the investigation of various properties of functions of generalized bounded variation. In particular, we obtain the following results: sharp relations between spaces of generalized bounded variation and spaces of functions defined by integral smoothness conditions (e.g., Sobolev and Besov spaces); optimal properties of certain scales of function spaces of frac tional smoothness generated by functionals of variational type; sharp embeddings within the scale of spaces of functions of bounded pvariation; results concerning bivariate functions of bounded pvariation, in particular sharp estimates of total variation in terms of the mixed Lpmodulus of continuity, and Fubinitype properties.

14 
Price models with weakly correlated processesRichter, Matthias, Starkloff, HansJörg, Wunderlich, Ralf 31 August 2004 (has links) (PDF)
Empirical autocorrelation functions of returns of stochastic price processes show
phenomena of correlation on small intervals of time, which decay to zero after a
short time. The paper deals with the concept of weakly correlated random processes to describe a mathematical model which takes into account this behaviour of
statistical data. Weakly correlated functions have been applied to model numerous
problems of physics and engineering. The main idea is, that the values of the functions at two points are uncorrelated if the distance between the points exceeds a
certain quantity epsilon > 0. In contrast to the white noise model, for distances smaller
than epsilon a correlation between the values is permitted.

15 
Lower semicontinuity and relaxation in BV of integrals with superlinear growthSoneji, Parth January 2012 (has links)
No description available.

16 
Cohomologia e propriedades estocásticas de transformações expansoras e observáveis lipschitzianos / Cohomology and stochastics properties of expanding maps and lipschitzians observablesAmanda de Lima 20 March 2007 (has links)
Provamos o Teorema do Limite Central para transformações expansoras por pedaços em um intervalo e observáveis com variação limitada. Utilizamos a abordagem desenvolvida por R. RousseauEgele, como apresentada por A. Broise. O método da demonstração se baseia no estudo de pertubações do operador de transferência de RuellePerronFrobenius. Uma contribuição original é dada no último capítulo, onde provamos que, para transformações markovianas expansoras, todos os observáveis não constantes, contínuos e com variação limitada não são infinitamente cohomólogos à zero, generalizando um resultado de Bamón, RiveraLetelier, Urzúa and Kiwi para observáveis lipschitzianos e transformações \'z POT. n\' . A demonstração se baseia na teoria dos operadores de RuellePerronFrobenius desenvolvida nos capítulos anteriores / We prove the Central Limit Theorem for piecewise expanding interval transformations and observables with bounded variation, using the approach of J.RousseauEgele as described by A. Broise. This approach makes use of pertubations of the socalled RuellePerronFrobenius transfer operator. An original contribution is given in the last chapter, where we prove that for Markovian expanding interval maps all observables which are non constant, continuous and have bounded variation are not infinitely cohomologous with zero, generalizing a result by Bamón, RiveraLetelier, Urzúa and Kiwi for Lipschitzian observables and the transformations \'z POT. n\' . Our demosntration uses the theory of RuellePerronFrobenius operators developed in the previos chapters

17 
Lower Semicontinuity and Young Measures for Integral Functionals with Linear GrowthJohan Filip Rindler, Johan Filip January 2011 (has links)
No description available.

18 
Le théorème de lebesgue sur la dérivabilité des fonctions à variation bornéeMombo Mingandza, Patrick Landry 01 1900 (has links)
Dans ce mémoire, nous traiterons du théorème de Lebesgue, un des plus frappants
et des plus importants de l'analyse mathématique ; à savoir qu'une fonction
à variation bornée est dérivable presque partout. Le but de ce travail est de fournir,
à part la démonstration souvent proposée dans les cours de la théorie de la
mesure, d'autres démonstrations élaborées avec des outils mathématiques plus
simples. Ma contribution a consisté essentiellement à détailler et à compléter ces
démonstrations, puis à inclure la plupart des figures pour une meilleure lisibilité.
Nous allons maintenant, pour ce théorème qui se présente sous d'autres variantes,
en proposer l'historique et trois démonstrations différentes. / In this dissertation, we will be handling a theorem of Lebesgue, one of the
most stricking and ultimate of mathematical analysis ; namely a function with
bounded variation has a derivative almost everywhere. The aim of our research is
to provide, apart from the proof usually offered in measure theory courses, other
demontrations achieved with more simple mathematical tools. My contribution
was primarily to simplify and to complete these demonstrations, to include the
most of the drawings in order to visualize what is being said. For this theorem,
which has other presentations, we will give now the history and three different
demonstrations.

19 
On The Generalizations And Properties Of Abramovichwickstead SpacesPolat, Faruk 01 November 2008 (has links) (PDF)
In this thesis, we study two problems. The first problem is to introduce the general version of AbramovichWickstead type spaces and investigate its order properties. In particular, we study the ideals, order bounded sets, disjointness properties, Dedekind completion and the norm properties of this Riesz space. We also define a new concrete example of Riesz spacevalued uniformly continuous functions, denoted by CDr0 which generalizes the original AbramovichWickstead space. It is also shown that similar spaces CD0 and CDw introduced earlier by Alpay and Ercan are decomposable latticenormed spaces. The second problem is related to analytic representations of different classes of dominated operators on these spaces. Our main representation theorems say that regular linear operators on CDr0 or linear dominated operators on CD0 may be represented as the sum of integration with respect to operatorvalued measure and summation operation. In the case when the operator is order continuous or bocontinuous, then these representations reduce to discrete parts.

20 
Le théorème de lebesgue sur la dérivabilité des fonctions à variation bornéeMombo Mingandza, Patrick Landry 01 1900 (has links)
Dans ce mémoire, nous traiterons du théorème de Lebesgue, un des plus frappants
et des plus importants de l'analyse mathématique ; à savoir qu'une fonction
à variation bornée est dérivable presque partout. Le but de ce travail est de fournir,
à part la démonstration souvent proposée dans les cours de la théorie de la
mesure, d'autres démonstrations élaborées avec des outils mathématiques plus
simples. Ma contribution a consisté essentiellement à détailler et à compléter ces
démonstrations, puis à inclure la plupart des figures pour une meilleure lisibilité.
Nous allons maintenant, pour ce théorème qui se présente sous d'autres variantes,
en proposer l'historique et trois démonstrations différentes. / In this dissertation, we will be handling a theorem of Lebesgue, one of the
most stricking and ultimate of mathematical analysis ; namely a function with
bounded variation has a derivative almost everywhere. The aim of our research is
to provide, apart from the proof usually offered in measure theory courses, other
demontrations achieved with more simple mathematical tools. My contribution
was primarily to simplify and to complete these demonstrations, to include the
most of the drawings in order to visualize what is being said. For this theorem,
which has other presentations, we will give now the history and three different
demonstrations.

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