Analyse de la régularité hölderienne : De la théorie à l'application à des séries temporelles de températures

Part 1 is divided in 3 chapters. Chapter 1 is devoted to the definition of the notion of Hölder exponent and its properties. Chapter 2 introduces the Hausdorff measure and dimension and their properties. Chapter 3 is about multiresolution analysis and the wavelet leaders method, the multifractal formalism used in Part 2. Part 2 consists of applications of the wavelet leaders method to analyze the Hölder regularity of some well-known functions (Chapter 4) and of surface air temperature time series (Chapter 5).