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Author : E. Seneta
Publisher : Unknown
Page : 128 pages
File Size : 48,7 Mb
Release : 1976-03
Category : Mathematics
ISBN : STANFORD:36105031690220
Author : E. Seneta
Publisher : Springer
Page : 118 pages
File Size : 43,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540381372
Author : Valeriĭ V. Buldygin,Karl-Heinz Indlekofer,Oleg I. Klesov,Josef G. Steinebach
Publisher : Springer
Page : 482 pages
File Size : 44,8 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9783319995373
One 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.
Author : Marek Kuczma,Bogdan Choczewski,Roman Ger
Publisher : Cambridge University Press
Page : 580 pages
File Size : 54,8 Mb
Release : 1990-07-27
Category : Mathematics
ISBN : 0521355613
A cohesive and comprehensive account of the modern theory of iterative functional equations. Many of the results included have appeared before only in research literature, making this an essential volume for all those working in functional equations and in such areas as dynamical systems and chaos, to which the theory is closely related. The authors introduce the reader to the theory and then explore the most recent developments and general results. Fundamental notions such as the existence and uniqueness of solutions to the equations are stressed throughout, as are applications of the theory to such areas as branching processes, differential equations, ergodic theory, functional analysis and geometry. Other topics covered include systems of linear and nonlinear equations of finite and infinite ORD various function classes, conjugate and commutable functions, linearization, iterative roots of functions, and special functional equations.
Author : N. H. Bingham,C. M. Goldie,J. L. Teugels
Publisher : Cambridge University Press
Page : 518 pages
File Size : 45,8 Mb
Release : 1989-06-15
Category : Mathematics
ISBN : 0521379431
A comprehensive account of the theory and applications of regular variation.
Author : Sidney I. Resnick
Publisher : Springer
Page : 334 pages
File Size : 48,8 Mb
Release : 2013-12-20
Category : Mathematics
ISBN : 9780387759531
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 : Aleksandr Alekseevich Borovkov
Publisher : Cambridge University Press
Page : 655 pages
File Size : 51,5 Mb
Release : 2008
Category : Asymptotic expansions
ISBN : 8210379456XXX
A comprehensive monograph presenting a unified systematic exposition of the large deviations theory for heavy-tailed random walks.
Author : Rafal Kulik,Philippe Soulier
Publisher : Springer Nature
Page : 677 pages
File Size : 42,7 Mb
Release : 2020-07-01
Category : Mathematics
ISBN : 9781071607374
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.
Author : Sidney I. Resnick
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 43,5 Mb
Release : 2007
Category : Business & Economics
ISBN : 9780387242729
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 : Michael B. Marcus,Jay Rosen
Publisher : Cambridge University Press
Page : 640 pages
File Size : 54,7 Mb
Release : 2006-07-24
Category : Mathematics
ISBN : 0521863007
A readable 2006 synthesis of three main areas in the modern theory of stochastic processes.
Author : Ondrej Dosly,Pavel Rehak
Publisher : Elsevier
Page : 533 pages
File Size : 54,6 Mb
Release : 2005-07-06
Category : Mathematics
ISBN : 9780080461236
The book presents a systematic and compact treatment of the qualitative theory of half-linear differential 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.
Author : Gareth W. Peters,Pavel V. Shevchenko
Publisher : John Wiley & Sons
Page : 667 pages
File Size : 48,9 Mb
Release : 2015-05-26
Category : Mathematics
ISBN : 9781118909539
ADVANCES IN HEAVY TAILED RISK MODELING A cutting-edge guide for the theories, applications, and statistical methodologies essential to heavy tailed risk modeling Focusing on the quantitative aspects of heavy tailed loss processes in operational risk and relevant insurance analytics, Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk presents comprehensive coverage of the latest research on the theories and applications in risk measurement and modeling techniques. Featuring a unique balance of mathematical and statistical perspectives, the handbook begins by introducing the motivation for heavy tailed risk processes. A companion with Fundamental Aspects of Operational Risk and Insurance Analytics: A Handbook of Operational Risk, the handbook provides a complete framework for all aspects of operational risk management and includes: Clear coverage on advanced topics such as splice loss models, extreme value theory, heavy tailed closed form loss distribution approach models, flexible heavy tailed risk models, risk measures, and higher order asymptotic approximations of risk measures for capital estimation An exploration of the characterization and estimation of risk and insurance modeling, which includes sub-exponential models, alpha-stable models, and tempered alpha stable models An extended discussion of the core concepts of risk measurement and capital estimation as well as the details on numerical approaches to evaluation of heavy tailed loss process model capital estimates Numerous detailed examples of real-world methods and practices of operational risk modeling used by both financial and non-financial institutions Advances in Heavy Tailed Risk Modeling: A Handbook of Operational Risk is an excellent reference for risk management practitioners, quantitative analysts, financial engineers, and risk managers. The handbook is also useful for graduate-level courses on heavy tailed processes, advanced risk management, and actuarial science.
Author : Pavle Mladenović
Publisher : Springer Nature
Page : 287 pages
File Size : 40,5 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9783031574122
Author : Allan Gut
Publisher : Springer Science & Business Media
Page : 617 pages
File Size : 55,8 Mb
Release : 2006-03-16
Category : Mathematics
ISBN : 9780387273327
This textbook on the theory of probability starts from the premise that rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by explanations of the three main subjects in probability: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales.
Author : Archil Gulisashvili
Publisher : Springer Science & Business Media
Page : 371 pages
File Size : 53,6 Mb
Release : 2012-09-04
Category : Mathematics
ISBN : 9783642312144
Asymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models, that have been developed as an answer to certain imperfections in a celebrated Black-Scholes model of option pricing. In a stock price model with stochastic volatility, the random behavior of the volatility is described by a stochastic process. For instance, in the Hull-White model the volatility process is a geometric Brownian motion, the Stein-Stein model uses an Ornstein-Uhlenbeck process as the stochastic volatility, and in the Heston model a Cox-Ingersoll-Ross process governs the behavior of the volatility. One of the author's main goals is to provide sharp asymptotic formulas with error estimates for distribution densities of stock prices, option pricing functions, and implied volatilities in various stochastic volatility models. The author also establishes sharp asymptotic formulas for the implied volatility at extreme strikes in general stochastic stock price models. The present volume is addressed to researchers and graduate students working in the area of financial mathematics, analysis, or probability theory. The reader is expected to be familiar with elements of classical analysis, stochastic analysis and probability theory.