Regular Variation PDF Download

Author: N. H. Bingham
Publisher: Cambridge University Press
ISBN: 9780521379434
Category : Mathematics
Languages : en
Pages : 518

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Book Description
A comprehensive account of the theory and applications of regular variation.

Author: Vojislav Maric
Publisher: Springer
ISBN: 3540465200
Category : Mathematics
Languages : en
Pages : 141

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Book Description
This is the first book offering an application of regular variation to the qualitative theory of differential equations. The notion of regular variation, introduced by Karamata (1930), extended by several scientists, most significantly de Haan (1970), is a powerful tool in studying asymptotics in various branches of analysis and in probability theory. Here, some asymptotic properties (including non-oscillation) of solutions of second order linear and of some non-linear equations are proved by means of a new method that the well-developed theory of regular variation has yielded. A good graduate course both in real analysis and in differential equations suffices for understanding the book.

Author: Sidney I. Resnick
Publisher: Springer
ISBN: 0387759530
Category : Mathematics
Languages : en
Pages : 334

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Book Description
This book examines the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors. It emphasizes the core primacy of three topics necessary for understanding extremes: the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces.

Author: E. Seneta
Publisher: Springer
ISBN: 3540381376
Category : Mathematics
Languages : en
Pages : 118

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Book Description

Author: Vojislav Maric
Publisher:
ISBN: 9783662213278
Category :
Languages : en
Pages : 144

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Book Description

Author: Sidney I. Resnick
Publisher: Springer Science & Business Media
ISBN: 0387450246
Category : Mathematics
Languages : en
Pages : 412

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Book Description
This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. It is uniquely devoted to heavy-tails and emphasizes both probability modeling and statistical methods for fitting models. Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use a statistics package. This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.

Author: Pavle Mladenović
Publisher: Springer Nature
ISBN: 3031574125
Category :
Languages : en
Pages : 287

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Book Description

Author: Thomas Meinguet
Publisher: Presses univ. de Louvain
ISBN: 287463235X
Category : Science
Languages : en
Pages : 173

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Book Description
The goal of this thesis is to treat the temporal tail dependence and the cross-sectional tail dependence of heavy tailed functional time series. Functional time series are aimed at modelling spatio-temporal phenomena; for instance rain, temperature, pollution on a given geographical area, with temporally dependent observations. Heavy tails mean that the series can exhibit much higher spikes than with Gaussian distributions for instance. In such cases, second moments cannot be assumed to exist, violating the basic assumption in standard functional data analysis based on the sequence of autocovariance operators. As for random variables, regular variation provides the mathematical backbone for a coherent theory of extreme values. The main tools introduced in this thesis for a regularly varying functional time series are its tail process and its spectral process. These objects capture all the aspects of the probability distribution of extreme values jointly over time and space. The development of the tail and spectral process for heavy tailed functional time series is followed by three theoretical applications. The first application is a characterization of a variety of indices and objects describing the extremal behavior of the series: the extremal index, tail dependence coefficients, the extremogram and the point process of extremes. The second is the computation of an explicit expression of the tail and spectral processes for heavy tailed linear functional time series. The third and final application is the introduction and the study of a model for the spatio-temporal dependence for functional time series called maxima of moving maxima of continuous functions (CM3 processes), with the development of an estimation method.

Author: Barbel Finkenstadt
Publisher: CRC Press
ISBN: 1135438013
Category : Mathematics
Languages : en
Pages : 424

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Book Description
Because of its potential to ...predict the unpredictable,... extreme value theory (EVT) and methodology is currently receiving a great deal of attention from statistical and mathematical researchers. This book brings together world-recognized authorities in their respective fields to provide expository chapters on the applications, use, and theory of extreme values in the areas of finance, insurance, the environment, and telecommunications. The comprehensive introductory chapter by Richard Smith ensures a high level of cohesion for this volume.

Author: Rafal Kulik
Publisher: Springer Nature
ISBN: 1071607375
Category : Mathematics
Languages : en
Pages : 677

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Book Description
This book aims to present a comprehensive, self-contained, and concise overview of extreme value theory for time series, incorporating the latest research trends alongside classical methodology. Appropriate for graduate coursework or professional reference, the book requires a background in extreme value theory for i.i.d. data and basics of time series. Following a brief review of foundational concepts, it progresses linearly through topics in limit theorems and time series models while including historical insights at each chapter’s conclusion. Additionally, the book incorporates complete proofs and exercises with solutions as well as substantive reference lists and appendices, featuring a novel commentary on the theory of vague convergence.