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.
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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.
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.
Regularly Varying Functions
Author: E. Seneta
Publisher: Springer
Published: 2006-11-14
Total Pages: 118
ISBN-13: 3540381376
DOWNLOAD EBOOKRegular Variation and Differential Equations
Author: Vojislav Maric
Publisher:
Published: 2014-01-15
Total Pages: 144
ISBN-13: 9783662213278
DOWNLOAD EBOOKMathematical Analysis and Applications
Author: Michael Ruzhansky
Publisher: John Wiley & Sons
Published: 2018-05-11
Total Pages: 764
ISBN-13: 1119414342
DOWNLOAD EBOOKAn authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.
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.
Heavy-Tail Phenomena
Author: Sidney I. Resnick
Publisher: Springer Science & Business Media
Published: 2007
Total Pages: 412
ISBN-13: 0387242724
DOWNLOAD EBOOKThis 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.
Limit Distributions for Sums of Independent Random Vectors
Author: Mark M. Meerschaert
Publisher: John Wiley & Sons
Published: 2001-07-11
Total Pages: 514
ISBN-13: 9780471356295
DOWNLOAD EBOOKDie Quintessenz aus über 100 Originalarbeiten! Ausgehend von den Grundpfeilern der modernen Wahrscheinlichkeitstheorie entwickeln die Autoren dieses in sich geschlossenen, gut verständlich formulierten Bandes die Theorie der unendlich teilbaren Verteilungen und der regulären Variation. Im Anschluss erarbeiten sie die allgemeine Grenzwerttheorie für unabhängige Zufallsvektoren. Dabei achten sie sorgfältig darauf, alle Aspekte in den Kontext der Wahrscheinlichkeitslehre und Statistik zu stellen und bieten dafür eine Fülle von Zusatzinformationen an.
Stochastic Processes and Long Range Dependence
Author: Gennady Samorodnitsky
Publisher: Springer
Published: 2016-11-09
Total Pages: 419
ISBN-13: 3319455753
DOWNLOAD EBOOKThis monograph is a gateway for researchers and graduate students to explore the profound, yet subtle, world of long-range dependence (also known as long memory). The text is organized around the probabilistic properties of stationary processes that are important for determining the presence or absence of long memory. The first few chapters serve as an overview of the general theory of stochastic processes which gives the reader sufficient background, language, and models for the subsequent discussion of long memory. The later chapters devoted to long memory begin with an introduction to the subject along with a brief history of its development, followed by a presentation of what is currently the best known approach, applicable to stationary processes with a finite second moment. The book concludes with a chapter devoted to the author’s own, less standard, point of view of long memory as a phase transition, and even includes some novel results. Most of the material in the book has not previously been published in a single self-contained volume, and can be used for a one- or two-semester graduate topics course. It is complete with helpful exercises and an appendix which describes a number of notions and results belonging to the topics used frequently throughout the book, such as topological groups and an overview of the Karamata theorems on regularly varying functions.
