Probability Approximations for Sums of Independent and Non-identically Distributed Random Variables PDF Download

Author: S. Vasudevan
Publisher:
ISBN:
Category :
Languages : en
Pages : 138

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Author: V.V. Petrov
Publisher: Springer Science & Business Media
ISBN: 3642658091
Category : Mathematics
Languages : en
Pages : 360

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Book Description
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: Boris Vladimirovich Gnedenko
Publisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 296

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Author: Vladimir M. Zolotarev
Publisher: Walter de Gruyter
ISBN: 3110936534
Category : Mathematics
Languages : en
Pages : 429

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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: Miklós Csörgö
Publisher: Wiley
ISBN: 9780471936350
Category : Mathematics
Languages : en
Pages : 464

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Explores probability and statistics from the ``Hungarian construction'' viewpoint. Concentrates on renewal and related processes, on weighted approximations of empirical and quantile processes and on the asymptotic distributions of functionals of these weighted processes. Also covers strong approximations of partial sums of independent identically distributed random variables and general quantile processes and their approximations in detail. Includes appendix and references.

Author: Boris V. Gnedenko
Publisher: CRC Press
ISBN: 100010267X
Category : Mathematics
Languages : en
Pages : 280

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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: Charles Stein
Publisher: IMS
ISBN: 9780940600089
Category : Mathematics
Languages : en
Pages : 172

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Author: Hans Fischer
Publisher: Springer Science & Business Media
ISBN: 0387878572
Category : Mathematics
Languages : en
Pages : 415

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This study discusses the history of the central limit theorem and related probabilistic limit theorems from about 1810 through 1950. In this context the book also describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The central limit theorem was originally deduced by Laplace as a statement about approximations for the distributions of sums of independent random variables within the framework of classical probability, which focused upon specific problems and applications. Making this theorem an autonomous mathematical object was very important for the development of modern probability theory.

Author: Aleksandr Alekseevich Borovkov
Publisher:
ISBN:
Category : Limit theorems (Probability theory)
Languages : en
Pages : 328

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Author: Yu.V. Prokhorov
Publisher: Springer
ISBN: 9783642081705
Category : Mathematics
Languages : en
Pages : 273

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Book Description
A collection of research level surveys on certain topics in probability theory by a well-known group of researchers. The book will be of interest to graduate students and researchers.