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Introduction Chapter 1. Multifractal theory How can phenomena be observed at different scales? The scale ratio Observations on and scales of hydrological processes Singularities A statistical description of multifractal processes The codimension function c(y) The statistical moments function K(q) General properties of multifractals Multifractals and extremes The divergence of moments Effect of the sample size Diagnosis on the presence of extreme values Description of multiplicative cascade models General description Properties of series generated by a multiplicative cascade Comment on conservative and non-conservative fields The universal multifractal model Comment on the estimation of universal multifractal parameters The universal multifractal model and extremes Chapter 2. Application of multifractals to rainfall and discharge series Data Multifractal analysis of rainfall and discharge series Spectral analysis Analysis of scale of moments laws Fitting the universal multifractal parameters Comment on extreme values Conclusion Acknowledgements Appendices Fractional integration and differentiation Table of notations used References List of authors

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