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Author : V. V. Buldygin
Publisher :
ISBN 13 : 9789401155694
Total Pages : 524 pages
Book Rating : 4.1/5 (556 download)
Download or read book Asymptotic Behaviour of Linearly Transformed Sums of Random Variables written by V. V. Buldygin and published by . This book was released on 1997-06-30 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : V.V. Buldygin
Publisher : Springer Science & Business Media
ISBN 13 : 9401155682
Total Pages : 512 pages
Book Rating : 4.4/5 (11 download)
Download or read book Asymptotic Behaviour of Linearly Transformed Sums of Random Variables written by V.V. Buldygin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop erties of almost all sample paths of the sequences involved (strong limit theorems). Although either of these directions is closely related to another one, each of them has its own range of specific problems, as well as the own methodology for solving the underlying problems. This book is devoted to the second of the above mentioned lines, which means that we study asymptotic behaviour of almost all sample paths of linearly transformed sums of independent random variables, vectors, and elements taking values in topological vector spaces. In the classical works of P.Levy, A.Ya.Khintchine, A.N.Kolmogorov, P.Hartman, A.Wintner, W.Feller, Yu.V.Prokhorov, and M.Loeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari ables was constructed. This theory not only provides conditions of the almost sure convergence of series of independent random variables, but also studies different ver sions of the strong law of large numbers and the law of the iterated logarithm. One should point out that, even in this traditional framework, there are still problems which remain open, while many definitive results have been obtained quite recently.
Author : Robert Qiu
Publisher : Springer Science & Business Media
ISBN 13 : 1461445442
Total Pages : 633 pages
Book Rating : 4.4/5 (614 download)
Download or read book Cognitive Networked Sensing and Big Data written by Robert Qiu and published by Springer Science & Business Media. This book was released on 2013-08-04 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wireless Distributed Computing and Cognitive Sensing defines high-dimensional data processing in the context of wireless distributed computing and cognitive sensing. This book presents the challenges that are unique to this area such as synchronization caused by the high mobility of the nodes. The author will discuss the integration of software defined radio implementation and testbed development. The book will also bridge new research results and contextual reviews. Also the author provides an examination of large cognitive radio network; hardware testbed; distributed sensing; and distributed computing.
Author : Nikolai Leonenko
Publisher : Springer Science & Business Media
ISBN 13 : 9780792356356
Total Pages : 418 pages
Book Rating : 4.3/5 (563 download)
Download or read book Limit Theorems for Random Fields with Singular Spectrum written by Nikolai Leonenko and published by Springer Science & Business Media. This book was released on 1999-02-28 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents limit theorems for nonlinear functionals of random fields with singular spectrum on the basis of various asymptotic expansions. This book will be of interest to mathematicians who use random fields in engineering or other applications.
Author : Ilya Molchanov
Publisher : Springer
ISBN 13 : 144717349X
Total Pages : 678 pages
Book Rating : 4.4/5 (471 download)
Download or read book Theory of Random Sets written by Ilya Molchanov and published by Springer. This book was released on 2017-12-14 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance. The present volume builds on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time fixes terminology and notation that often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development. It is completely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. Aimed at research level, Theory of Random Sets will be an invaluable reference for probabilists; mathematicians working in convex and integral geometry, set-valued analysis, capacity and potential theory; mathematical statisticians in spatial statistics and uncertainty quantification; specialists in mathematical economics, econometrics, decision theory, and mathematical finance; and electronic and electrical engineers interested in image analysis.
Author : Valeriĭ Vladimirovich Buldygin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821897911
Total Pages : 276 pages
Book Rating : 4.8/5 (979 download)
Download or read book Metric Characterization of Random Variables and Random Processes written by Valeriĭ Vladimirovich Buldygin and published by American Mathematical Soc.. This book was released on 2000-01-01 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic covered in this book is the study of metric and other close characteristics of different spaces and classes of random variables and the application of the entropy method to the investigation of properties of stochastic processes whose values, or increments, belong to given spaces. The following processes appear in detail: pre-Gaussian processes, shot noise processes representable as integrals over processes with independent increments, quadratically Gaussian processes, and, in particular, correlogram-type estimates of the correlation function of a stationary Gaussian process, jointly strictly sub-Gaussian processes, etc. The book consists of eight chapters divided into four parts: The first part deals with classes of random variables and their metric characteristics. The second part presents properties of stochastic processes "imbedded" into a space of random variables discussed in the first part. The third part considers applications of the general theory. The fourth part outlines the necessary auxiliary material. Problems and solutions presented show the intrinsic relation existing between probability methods, analytic methods, and functional methods in the theory of stochastic processes. The concluding sections, "Comments" and "References", gives references to the literature used by the authors in writing the book.
Author : Vladimir I. Bogachev
Publisher : American Mathematical Soc.
ISBN 13 : 147044738X
Total Pages : 286 pages
Book Rating : 4.4/5 (74 download)
Download or read book Weak Convergence of Measures written by Vladimir I. Bogachev and published by American Mathematical Soc.. This book was released on 2018-09-27 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.
Author : V.I. Bogachev
Publisher : Springer
ISBN 13 : 3319571176
Total Pages : 456 pages
Book Rating : 4.3/5 (195 download)
Download or read book Topological Vector Spaces and Their Applications written by V.I. Bogachev and published by Springer. This book was released on 2017-05-16 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. Overall, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.
Author : Vladimir V. Kalashnikov
Publisher : Springer Science & Business Media
ISBN 13 : 9401716935
Total Pages : 285 pages
Book Rating : 4.4/5 (17 download)
Download or read book Geometric Sums: Bounds for Rare Events with Applications written by Vladimir V. Kalashnikov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews problems associated with rare events arising in a wide range of circumstances, treating such topics as how to evaluate the probability an insurance company will be bankrupted, the lifetime of a redundant system, and the waiting time in a queue. Well-grounded, unique mathematical evaluation methods of basic probability characteristics concerned with rare events are presented, which can be employed in real applications, as the volume also contains relevant numerical and Monte Carlo methods. The various examples, tables, figures and algorithms will also be appreciated. Audience: This work will be useful to graduate students, researchers and specialists interested in applied probability, simulation and operations research.
Author : A. A. Borovkov
Publisher : Cambridge University Press
ISBN 13 : 1108901204
Total Pages : 437 pages
Book Rating : 4.1/5 (89 download)
Download or read book Asymptotic Analysis of Random Walks written by A. A. Borovkov and published by Cambridge University Press. This book was released on 2020-10-29 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.
Author : A.A. Borovkov
Publisher : Cambridge University Press
ISBN 13 : 1107074681
Total Pages : 437 pages
Book Rating : 4.1/5 (7 download)
Download or read book Asymptotic Analysis of Random Walks: Light-Tailed Distributions written by A.A. Borovkov and published by Cambridge University Press. This book was released on 2020-10-29 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic modern treatise on large deviation theory for random walks with light tails, from one of its key creators.
Author :
Publisher :
ISBN 13 :
Total Pages : 472 pages
Book Rating : 4.F/5 ( download)
Download or read book Abstracts of Communications written by and published by . This book was released on 1998 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : V.V. Petrov
Publisher : Springer Science & Business Media
ISBN 13 : 3642658091
Total Pages : 360 pages
Book Rating : 4.6/5 (426 download)
Download or read book Sums of Independent Random Variables written by V.V. Petrov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classic "Limit Dislribntions fOT slt1ns of Independent Ramdorn Vari ables" by B.V. Gnedenko and A.N. Kolmogorov was published in 1949. Since then the theory of summation of independent variables has devel oped rapidly. Today a summing-up of the studies in this area, and their results, would require many volumes. The monograph by I.A. Ibragi mov and Yu. V. I~innik, "Independent and Stationarily Connected VaTiables", which appeared in 1965, contains an exposition of the contem porary state of the theory of the summation of independent identically distributed random variables. The present book borders on that of Ibragimov and Linnik, sharing only a few common areas. Its main focus is on sums of independent but not necessarily identically distri buted random variables. It nevertheless includes a number of the most recent results relating to sums of independent and identically distributed variables. Together with limit theorems, it presents many probahilistic inequalities for sums of an arbitrary number of independent variables. The last two chapters deal with the laws of large numbers and the law of the iterated logarithm. These questions were not treated in Ibragimov and Linnik; Gnedenko and KolmogoTOv deals only with theorems on the weak law of large numbers. Thus this book may be taken as complementary to the book by Ibragimov and Linnik. I do not, however, assume that the reader is familiar with the latter, nor with the monograph by Gnedenko and Kolmogorov, which has long since become a bibliographical rarity
Author :
Publisher :
ISBN 13 :
Total Pages : 3096 pages
Book Rating : 4.3/5 (91 download)
Download or read book Whitaker's Books in Print written by and published by . This book was released on 1998 with total page 3096 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Boris V. Gnedenko
Publisher : CRC Press
ISBN 13 : 100010267X
Total Pages : 280 pages
Book Rating : 4.0/5 (1 download)
Download or read book Random Summation written by Boris V. Gnedenko and published by CRC Press. This book was released on 2020-07-24 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of its applications to solving practical problems in hardware and software reliability, insurance, finance, and more. The authors show how practice interacts with theory, and how new mathematical formulations of problems appear and develop. Attention is mainly focused on transfer theorems, description of the classes of limit laws, and criteria for convergence of distributions of sums for a random number of random variables. Theoretical background is given for the choice of approximations for the distribution of stock prices or surplus processes. General mathematical theory of reliability growth of modified systems, including software, is presented. Special sections deal with doubling with repair, rarefaction of renewal processes, limit theorems for supercritical Galton-Watson processes, information properties of probability distributions, and asymptotic behavior of doubly stochastic Poisson processes. Random Summation: Limit Theorems and Applications will be of use to specialists and students in probability theory, mathematical statistics, and stochastic processes, as well as to financial mathematicians, actuaries, and to engineers desiring to improve probability models for solving practical problems and for finding new approaches to the construction of mathematical models.
Author : V. V. Sazonov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3112313623
Total Pages : 720 pages
Book Rating : 4.1/5 (123 download)
Download or read book Proceedings of the Bakuriani Colloquium in Honour of Yu.V. Prohorov, Bakuriani, Georgia, USSR, 24 February–4 March, 1990 written by V. V. Sazonov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-05 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Proceedings of the Bakuriani Colloquium in Honour of Yu.V. Prohorov, Bakuriani, Georgia, USSR, 24 February-4 March, 1990".
Author :
Publisher :
ISBN 13 :
Total Pages : 1026 pages
Book Rating : 4.E/5 ( download)
Download or read book International Mathematical News written by and published by . This book was released on 1997 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt:
