Random Summation
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Random Summation
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Author : Boris V. Gnedenko
language : en
Publisher: CRC Press
Release Date : 2020-07-24
Random Summation written by Boris V. Gnedenko and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-24 with Mathematics categories.
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.
Sums Of Independent Random Variables
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Author : V.V. Petrov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Sums Of Independent Random Variables written by V.V. Petrov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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
Modern Theory Of Summation Of Random Variables
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Author : Vladimir M. Zolotarev
language : en
Publisher: Walter de Gruyter
Release Date : 2011-09-06
Modern Theory Of Summation Of Random Variables written by Vladimir M. Zolotarev and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-06 with Mathematics categories.
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.
Random Sums And Branching Stochastic Processes
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Author : Ibrahim Rahimov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Random Sums And Branching Stochastic Processes written by Ibrahim Rahimov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.
Modern Theory Of Summation Of Random Variables
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Author : V. M. Zolotarev
language : en
Publisher:
Release Date :
Modern Theory Of Summation Of Random Variables written by V. M. Zolotarev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Uniform Limit Theorems For Sums Of Independent Random Variables
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Author : Taĭvo Viktorovich Arak
language : en
Publisher: American Mathematical Soc.
Release Date : 1988
Uniform Limit Theorems For Sums Of Independent Random Variables written by Taĭvo Viktorovich Arak and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Among the diverse constructions studied in modern probability theory, the scheme for summation of independent random variables occupies a special place. This book presents a study of distributions of sums of independent random variables with minimal restrictions imposed on their distributions.
Sums Of Independent Random Variables
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Author : Valentin Vladimirovich Petrov
language : en
Publisher:
Release Date : 1975
Sums Of Independent Random Variables written by Valentin Vladimirovich Petrov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Distribution (Probability theory) categories.
On The Central Limit Theorem For The Sum Of A Random Number Of Independent Random Variables
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Author : J. R. Blum
language : en
Publisher:
Release Date : 1963
On The Central Limit Theorem For The Sum Of A Random Number Of Independent Random Variables written by J. R. Blum and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Asymptotic distribution (Probability theory) categories.
The Distribution And Properties Of A Weighted Sum Of Chi Squares
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Author : A. H. Feiveson
language : en
Publisher:
Release Date : 1968
The Distribution And Properties Of A Weighted Sum Of Chi Squares written by A. H. Feiveson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Distribution (Probability theory) categories.
A Road To Randomness In Physical Systems
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Author : Eduardo Engel
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-02-21
A Road To Randomness In Physical Systems written by Eduardo Engel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-21 with Mathematics categories.
There are many ways of introducing the concept of probability in classical, deterministic physics. This volume is concerned with one approach, known as 'the method of arbitrary functions', which was first considered by Poincare. Essentially, the method proceeds by associating some uncertainty to our knowledge of both the initial conditions and the values of the physical constants that characterize the evolution of a physical system. By modeling this uncertainty by a probability density distribution, it is then possible to analyze how the state of the system evolves through time. This approach may be applied to a wide variety of classical problems and the author considers here examples as diverse as bouncing balls, simple and coupled harmonic oscillators, integrable systems (such as spinning tops), planetary motion, and billiards. An important aspect of this account is to study the speed of convergence for solutions in order to determine the practical relevance of the method of arbitrary functions for specific examples. Consequently, both new results on convergence, and tractable upper bounds are derived and applied.