Extreme Values, Regular Variation and Point Processes
Extreme Values, Regular Variation and Point Processes

Author: Sidney I. Resnick

Publisher: Springer

Published: 2013-12-20

Total Pages: 334

ISBN-13: 0387759530

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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.

Regular Variation
Regular Variation

Author: N. H. Bingham

Publisher: Cambridge University Press

Published: 1989-06-15

Total Pages: 518

ISBN-13: 9780521379434

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

Heavy-Tailed Time Series
Heavy-Tailed Time Series

Author: Rafal Kulik

Publisher: Springer Nature

Published: 2020-07-01

Total Pages: 677

ISBN-13: 1071607375

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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.

Advanced R
Advanced R

Author: Hadley Wickham

Publisher: CRC Press

Published: 2015-09-15

Total Pages: 669

ISBN-13: 1498759807

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An Essential Reference for Intermediate and Advanced R Programmers Advanced R presents useful tools and techniques for attacking many types of R programming problems, helping you avoid mistakes and dead ends. With more than ten years of experience programming in R, the author illustrates the elegance, beauty, and flexibility at the heart of R. The book develops the necessary skills to produce quality code that can be used in a variety of circumstances. You will learn: The fundamentals of R, including standard data types and functions Functional programming as a useful framework for solving wide classes of problems The positives and negatives of metaprogramming How to write fast, memory-efficient code This book not only helps current R users become R programmers but also shows existing programmers what’s special about R. Intermediate R programmers can dive deeper into R and learn new strategies for solving diverse problems while programmers from other languages can learn the details of R and understand why R works the way it does.

Half-Linear Differential Equations
Half-Linear Differential Equations

Author: Ondrej Dosly

Publisher: Elsevier

Published: 2005-07-06

Total Pages: 533

ISBN-13: 0080461239

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The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE's with p-Laplacian, half-linear difference equations and various more general nonlinear differential equations.- The first complete treatment of the qualitative theory of half-linear differential equations.- Comparison of linear and half-linear theory.- Systematic approach to half-linear oscillation and asymptotic theory.- Comprehensive bibliography and index.- Useful as a reference book in the topic.

Operator Theory and Harmonic Analysis
Operator Theory and Harmonic Analysis

Author: Alexey N. Karapetyants

Publisher: Springer Nature

Published: 2021-08-31

Total Pages: 413

ISBN-13: 3030768295

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This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the second in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University, Rostov-on-Don, Russia. This volume focuses on mathematical methods and applications of probability and statistics in the context of general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multi-parameter objects required when considering operators and objects with variable parameters.

The Fundamentals of Heavy Tails
The Fundamentals of Heavy Tails

Author: Jayakrishnan Nair

Publisher: Cambridge University Press

Published: 2022-06-09

Total Pages: 266

ISBN-13: 1009062964

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Heavy tails –extreme events or values more common than expected –emerge everywhere: the economy, natural events, and social and information networks are just a few examples. Yet after decades of progress, they are still treated as mysterious, surprising, and even controversial, primarily because the necessary mathematical models and statistical methods are not widely known. This book, for the first time, provides a rigorous introduction to heavy-tailed distributions accessible to anyone who knows elementary probability. It tackles and tames the zoo of terminology for models and properties, demystifying topics such as the generalized central limit theorem and regular variation. It tracks the natural emergence of heavy-tailed distributions from a wide variety of general processes, building intuition. And it reveals the controversy surrounding heavy tails to be the result of flawed statistics, then equips readers to identify and estimate with confidence. Over 100 exercises complete this engaging package.