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This book provides a general treatment of a class of functionals modelled on convolution energies with kernel having finite p-moments. A general asymptotic analysis of such non-local functionals is performed, via Gamma-convergence, in order to show that the limit may be a local functional representable as an integral. Energies of this form are encountered in many different contexts and the interest in building up a general theory is also motivated by the multiple interests in applications (e.g. peridynamics theory, population dynamics phenomena and data science). The results obtained are applied to periodic and stochastic homogenization, perforated domains, gradient flows, and point-clouds models. This book is mainly intended for mathematical analysts and applied mathematicians who are also interested in exploring further applications of the theory to pass from a non-local to a local description, both in static problems and in dynamic problems. .

Algebra --- Functional analysis --- Numerical methods of optimisation --- Operational research. Game theory --- algebra --- analyse (wiskunde) --- functies (wiskunde) --- wiskunde --- kansrekening --- optimalisatie --- Convolutions (Mathematics) --- Variational principles. --- Convolucions (Matemàtica) --- Principis variacionals

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Smoothness of functions. --- Smooth functions --- Functions --- Funcions --- Càlcul diferencial --- Càlcul --- Càlcul integral --- Funcions (Matemàtica) --- Funcions matemàtiques --- Anàlisi matemàtica --- Teoria de conjunts --- Aplicacions (Matemàtica) --- Constants matemàtiques --- Convergència (Matemàtica) --- Convolucions (Matemàtica) --- Funcions algebraiques --- Funcions contínues --- Funcions discontínues --- Funcions d'ona --- Funcions especials --- Teoria de l'aproximació --- Superfícies de Riemann

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Convolutions (Mathematics) --- Differential operators. --- Diffusion processes. --- Markov processes --- Operators, Differential --- Differential equations --- Operator theory --- Convolution transforms --- Transformations, Convolution --- Distribution (Probability theory) --- Functions --- Integrals --- Transformations (Mathematics) --- Convolucions (Matemàtica) --- Operadors diferencials --- Processos de difusió --- Processos de Markov --- Teoria d'operadors --- Geometria espectral --- Operador de Schrödinger --- Transformacions de convolució --- Transformades de convolució --- Distribució (Teoria de la probabilitat) --- Funcions --- Transformacions (Matemàtica)

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This book presents the state of the art in extreme value theory, with a collection of articles related to a seminal paper on the bivariate extreme value distribution written by Professor Masaaki Sibuya in 1960, demonstrating various developments of the original idea over the last half-century. Written by active researchers, the unique combination of articles allows readers to gain a sense of the excellence of the field, ranging from theory to practice, and the tradition of theoretical developments motivated by practically important issues such as tsunamis and financial crises. The contributions discuss a range of topics, including the parameter estimation of the generalized beta distribution, resampling with the empirical beta copula, and regression analysis on imbalanced binary data, as well as the semiparametric estimation of the upper bound of extrema, the long-term analysis of extreme precipitation over Japanese river basins, and various rules of thumb in hydrology.

Statistics . --- Econometrics. --- Applied Statistics. --- Statistical Theory and Methods. --- Economics, Mathematical --- Statistics --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Extreme value theory. --- Distribution (Probability theory) --- Random variables --- Distribució (Teoria de la probabilitat) --- Distribució (Anàlisi matemàtica) --- Distribució de freqüències --- Funcions de distribució --- Probabilitats --- Bootstrap (Estadística) --- Convolucions (Matemàtica) --- Corbes de freqüències --- Distribució de Gauss --- Distribució de Gauss inversa --- Estadística robusta --- Famílies exponencials (Estadística) --- Mesures de probabilitats --- Mètode dels moments (Estadística) --- Processos gaussians --- Tests d'hipòtesi (Estadística) --- Funcions característiques

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Functions --- Approximation theory --- Approximation theory. --- Functions. --- Analysis (Mathematics) --- Theory of approximation --- Differential equations --- Mathematical analysis --- Mathematics --- Numbers, Complex --- Set theory --- Calculus --- Functional analysis --- Polynomials --- Chebyshev systems --- Funcions. --- Teoria de l'aproximació. --- Anàlisi funcional --- Funcions --- Polinomis --- Anàlisi numèrica --- Aproximació diofàntica --- Aproximació estocàstica --- Aproximants de Padé --- Interpolació (Matemàtica) --- Pertorbació (Matemàtica) --- Sistemes de Txebixov --- Funcions (Matemàtica) --- Funcions matemàtiques --- Anàlisi matemàtica --- Teoria de conjunts --- Aplicacions (Matemàtica) --- Constants matemàtiques --- Convergència (Matemàtica) --- Convolucions (Matemàtica) --- Funcions algebraiques --- Funcions contínues --- Funcions discontínues --- Funcions d'ona --- Funcions especials --- Teoria de l'aproximació --- Superfícies de Riemann --- Càlcul