Regularly Varying Functions
Author: E. Seneta
Publisher: Springer
Published: 2006-11-14
Total Pages: 118
ISBN-13: 3540381376
DOWNLOAD EBOOKPosts
Regular Variation
Author: N. H. Bingham
Publisher: Cambridge University Press
Published: 1989-06-15
Total Pages: 518
ISBN-13: 9780521379434
DOWNLOAD EBOOKA comprehensive account of the theory and applications of regular variation.
Extreme Values, Regular Variation and Point Processes
Author: Sidney I. Resnick
Publisher: Springer
Published: 2013-12-20
Total Pages: 334
ISBN-13: 0387759530
DOWNLOAD EBOOKThis 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.
Heavy-Tailed Time Series
Author: Rafal Kulik
Publisher: Springer Nature
Published: 2020-07-01
Total Pages: 677
ISBN-13: 1071607375
DOWNLOAD EBOOKThis 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.
Pseudo-Regularly Varying Functions and Generalized Renewal Processes
Author: Valeriĭ V. Buldygin
Publisher: Springer
Published: 2018-10-12
Total Pages: 496
ISBN-13: 3319995375
DOWNLOAD EBOOKOne of the main aims of this book is to exhibit some fruitful links between renewal theory and regular variation of functions. Applications of renewal processes play a key role in actuarial and financial mathematics as well as in engineering, operations research and other fields of applied mathematics. On the other hand, regular variation of functions is a property that features prominently in many fields of mathematics. The structure of the book reflects the historical development of the authors’ research work and approach – first some applications are discussed, after which a basic theory is created, and finally further applications are provided. The authors present a generalized and unified approach to the asymptotic behavior of renewal processes, involving cases of dependent inter-arrival times. This method works for other important functionals as well, such as first and last exit times or sojourn times (also under dependencies), and it can be used to solve several other problems. For example, various applications in function analysis concerning Abelian and Tauberian theorems can be studied as well as those in studies of the asymptotic behavior of solutions of stochastic differential equations. The classes of functions that are investigated and used in a probabilistic context extend the well-known Karamata theory of regularly varying functions and thus are also of interest in the theory of functions. The book provides a rigorous treatment of the subject and may serve as an introduction to the field. It is aimed at researchers and students working in probability, the theory of stochastic processes, operations research, mathematical statistics, the theory of functions, analytic number theory and complex analysis, as well as economists with a mathematical background. Readers should have completed introductory courses in analysis and probability theory.
Advanced R
Author: Hadley Wickham
Publisher: CRC Press
Published: 2015-09-15
Total Pages: 669
ISBN-13: 1498759807
DOWNLOAD EBOOKAn 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
Author: Ondrej Dosly
Publisher: Elsevier
Published: 2005-07-06
Total Pages: 533
ISBN-13: 0080461239
DOWNLOAD EBOOKThe 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.
Regular Variation and Differential Equations
Author: Vojislav Maric
Publisher: Springer
Published: 2007-05-06
Total Pages: 141
ISBN-13: 3540465200
DOWNLOAD EBOOKThis 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.
asymptotic analysis of random walks
Author: Aleksandr Alekseevich Borovkov
Publisher: Cambridge University Press
Published: 2008
Total Pages: 655
ISBN-13:
DOWNLOAD EBOOKA comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.
Operator Theory and Harmonic Analysis
Author: Alexey N. Karapetyants
Publisher: Springer Nature
Published: 2021-08-31
Total Pages: 413
ISBN-13: 3030768295
DOWNLOAD EBOOKThis 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.
