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| Author | : Arsen L. Yakimiv |
| Publisher | : Walter de Gruyter |
| Total Pages | : 236 |
| Release | : 2012-03-20 |
| Genre | : Mathematics |
| ISBN | : 3110195291 |
The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
| Author | : Arsen Li︠u︡bomirovich I︠A︡kymiv |
| Publisher | : |
| Total Pages | : 233 |
| Release | : 2005 |
| Genre | : Differential equations, Elliptic |
| ISBN | : 9789047411956 |
The Tauberian theory has found a widespread application in probability theory. Despite the strong interest of probabilists in Tauberian theorems, no book specially devoted to this topic has been published yet. This monograph is intended to fill this gap.
| Author | : Alekseĭ Georgievich Postnikov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 150 |
| Release | : 1980 |
| Genre | : Mathematics |
| ISBN | : 9780821830482 |
| Author | : Jacob Korevaar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 497 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662102250 |
Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the beginning and his expert commentary evokes the excitement surrounding the early results. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory. There are the spectacular "high-indices" theorems and Karamata's "regular variation", which permeates probability theory. The author presents Gelfand's elegant algebraic treatment of Wiener theory and his own distributional approach. There is also a new unified theory for Borel and "circle" methods. The text describes many Tauberian ways to the prime number theorem. A large bibliography and a substantial index round out the book.
| Author | : Willliam Feller |
| Publisher | : John Wiley & Sons |
| Total Pages | : 708 |
| Release | : 2008-08 |
| Genre | : |
| ISBN | : 9788126518067 |
· The Exponential and the Uniform Densities· Special Densities. Randomization· Densities in Higher Dimensions. Normal Densities and Processes· Probability Measures and Spaces· Probability Distributions in Rr· A Survey of Some Important Distributions and Processes· Laws of Large Numbers. Applications in Analysis· The Basic Limit Theorems· Infinitely Divisible Distributions and Semi-Groups· Markov Processes and Semi-Groups· Renewal Theory· Random Walks in R1· Laplace Transforms. Tauberian Theorems. Resolvents· Applications of Laplace Transforms· Characteristic Functions· Expansions Related to the Central Limit Theorem,· Infinitely Divisible Distributions· Applications of Fourier Methods to Random Walks· Harmonic Analysis
| Author | : Alexander Zeifman |
| Publisher | : MDPI |
| Total Pages | : 370 |
| Release | : 2021-03-05 |
| Genre | : Mathematics |
| ISBN | : 3036504524 |
The aim of this Special Issue of Mathematics is to commemorate the outstanding Russian mathematician Vladimir Zolotarev, whose 90th birthday will be celebrated on February 27th, 2021. The present Special Issue contains a collection of new papers by participants in sessions of the International Seminar on Stability Problems for Stochastic Models founded by Zolotarev. Along with research in probability distributions theory, limit theorems of probability theory, stochastic processes, mathematical statistics, and queuing theory, this collection contains papers dealing with applications of stochastic models in modeling of pension schemes, modeling of extreme precipitation, construction of statistical indicators of scientific publication importance, and other fields.
| Author | : Sidney I. Resnick |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 412 |
| Release | : 2007-12-03 |
| Genre | : Mathematics |
| ISBN | : 0387450246 |
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 | : Aleksandr Vadimovich Bulinskii |
| Publisher | : World Scientific |
| Total Pages | : 447 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 981270941X |
This volume is devoted to the study of asymptotic properties of wide classes of stochastic systems arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided. For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications. There are 434 items in the bibliography. The book is self-contained, provides detailed proofs, for reader's convenience some auxiliary results are included in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.). Contents: Random Systems with Covariance Inequalities; Moment and Maximal Inequalities; Central Limit Theorem; Almost Sure Convergence; Invariance Principles; Law of the Iterated Logarithm; Statistical Applications; Integral Functionals. Readership: Researchers in modern probability and statistics, graduate students and academic staff of the universities.
| Author | : Valeriĭ V. Buldygin |
| Publisher | : Springer |
| Total Pages | : 482 |
| Release | : 2018-10-12 |
| Genre | : Mathematics |
| ISBN | : 3319995375 |
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 | : Patrick Billingsley |
| Publisher | : SIAM |
| Total Pages | : 37 |
| Release | : 1971-01-01 |
| Genre | : Mathematics |
| ISBN | : 9781611970623 |
A treatment of the convergence of probability measures from the foundations to applications in limit theory for dependent random variables. Mapping theorems are proved via Skorokhod's representation theorem; Prokhorov's theorem is proved by construction of a content. The limit theorems at the conclusion are proved under a new set of conditions that apply fairly broadly, but at the same time make possible relatively simple proofs.
