A Few Limit Theorems For Sums Of Independent Random Variables

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Sums of Independent Random Variables

Author : V.V. Petrov
Publisher : Springer Science & Business Media
ISBN 13 : 3642658091
Total Pages : 360 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Sums of Independent Random Variables by : V.V. Petrov

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

Limit Distributions for Sums of Independent Random Variables

Author : B V (Boris Vladimirovich) Gnedenko
Publisher : Hassell Street Press
ISBN 13 : 9781014649485
Total Pages : 284 pages
Book Rating : 4.6/5 (494 download)

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Book Synopsis Limit Distributions for Sums of Independent Random Variables by : B V (Boris Vladimirovich) Gnedenko

Download or read book Limit Distributions for Sums of Independent Random Variables written by B V (Boris Vladimirovich) Gnedenko and published by Hassell Street Press. This book was released on 2021-09-09 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Limit Theorems of Probability Theory

Author : Yu.V. Prokhorov
Publisher : Springer Science & Business Media
ISBN 13 : 3662041723
Total Pages : 280 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Limit Theorems of Probability Theory by : Yu.V. Prokhorov

Download or read book Limit Theorems of Probability Theory written by Yu.V. Prokhorov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

On the Central Limit Theorem for the Sum of a Random Number of Independent Random Variables

Author : J. R. Blum
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis On the Central Limit Theorem for the Sum of a Random Number of Independent Random Variables by : J. R. Blum

Download or read book On the Central Limit Theorem for the Sum of a Random Number of Independent Random Variables written by J. R. Blum and published by . This book was released on 1963 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Probability, Finance and Insurance

Author : T. L. Lai
Publisher : World Scientific
ISBN 13 : 9812702717
Total Pages : 253 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Probability, Finance and Insurance by : T. L. Lai

Download or read book Probability, Finance and Insurance written by T. L. Lai and published by World Scientific. This book was released on 2004 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This workshop was the first of its kind in bringing together researchers in probability theory, stochastic processes, insurance and finance from mainland China, Taiwan, Hong Kong, Singapore, Australia and the United States. In particular, as China has joined the WTO, there is a growing demand for expertise in actuarial sciences and quantitative finance. The strong probability research and graduate education programs in many of China's universities can be enriched by their outreach in fields that are of growing importance to the country's expanding economy, and the workshop and its proceedings can be regarded as the first step in this direction. This book presents the most recent developments in probability, finance and actuarial sciences, especially in Chinese probability research. It focuses on the integration of probability theory with applications in finance and insurance. It also brings together academic researchers and those in industry and government. With contributions by leading authorities on probability theory OCo particularly limit theory and large derivations, valuation of credit derivatives, portfolio selection, dynamic protection and ruin theory OCo it is an essential source of ideas and information for graduate students and researchers in probability theory, mathematical finance and actuarial sciences, and thus every university should acquire a copy. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo Index to Social Sciences & Humanities Proceedings- (ISSHP- / ISI Proceedings). OCo Index to Social Sciences & Humanities Proceedings (ISSHP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences. Contents: Limit Theorems for Moving Averages (T L Lai); On Large Deviations for Moving Average Processes (L Wu); Recent Progress on Self-Normalized Limit Theorems (Q-M Shao); Limit Theorems for Independent Self-Normalized Sums (B-Y Jing); Phase Changes in Random Recursive Structures and Algorithms (H-K Hwang); JohnsonOCoMehl Tessellations: Asymptotics and Inferences (S N Chiu); Rapid Simulation of Correlated Defaults and the Valuation of Basket Default Swaps (Z Zhang et al.); Dynamic Protection with Optimal Withdrawal (H U Gerber & E S W Shiu); Ruin Probability for a Model Under Markovian Switching Regime (H Yang & G Yin); and other papers. Readership: Researchers and graduate students in probability and statistics."

Bernoulli, 1713 ; Bayes, 1763 ; Laplace, 1913

Author : Jerzy Neyman
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (243 download)

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Book Synopsis Bernoulli, 1713 ; Bayes, 1763 ; Laplace, 1913 by : Jerzy Neyman

Download or read book Bernoulli, 1713 ; Bayes, 1763 ; Laplace, 1913 written by Jerzy Neyman and published by . This book was released on 1965 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Uniform Limit Theorems for Sums of Independent Random Variables

Author : Taĭvo Viktorovich Arak
Publisher : American Mathematical Soc.
ISBN 13 : 9780821831182
Total Pages : 236 pages
Book Rating : 4.8/5 (311 download)

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Book Synopsis Uniform Limit Theorems for Sums of Independent Random Variables by : Taĭvo Viktorovich Arak

Download or read book Uniform Limit Theorems for Sums of Independent Random Variables written by Taĭvo Viktorovich Arak and published by American Mathematical Soc.. This book was released on 1988 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

High-Dimensional Probability

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Martingale Limit Theory and Its Application

Author : P. Hall
Publisher : Academic Press
ISBN 13 : 1483263223
Total Pages : 321 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Martingale Limit Theory and Its Application by : P. Hall

Download or read book Martingale Limit Theory and Its Application written by P. Hall and published by Academic Press. This book was released on 2014-07-10 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.

Probability Inequalities

Author : Zhengyan Lin
Publisher : Springer Science & Business Media
ISBN 13 : 3642052614
Total Pages : 192 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Probability Inequalities by : Zhengyan Lin

Download or read book Probability Inequalities written by Zhengyan Lin and published by Springer Science & Business Media. This book was released on 2011-05-30 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inequality has become an essential tool in many areas of mathematical research, for example in probability and statistics where it is frequently used in the proofs. "Probability Inequalities" covers inequalities related with events, distribution functions, characteristic functions, moments and random variables (elements) and their sum. The book shall serve as a useful tool and reference for scientists in the areas of probability and statistics, and applied mathematics. Prof. Zhengyan Lin is a fellow of the Institute of Mathematical Statistics and currently a professor at Zhejiang University, Hangzhou, China. He is the prize winner of National Natural Science Award of China in 1997. Prof. Zhidong Bai is a fellow of TWAS and the Institute of Mathematical Statistics; he is a professor at the National University of Singapore and Northeast Normal University, Changchun, China.

Independent and Stationary Sequences of Random Variables

Author : Ilʹdar Abdulovich Ibragimov
Publisher :
ISBN 13 :
Total Pages : 456 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Independent and Stationary Sequences of Random Variables by : Ilʹdar Abdulovich Ibragimov

Download or read book Independent and Stationary Sequences of Random Variables written by Ilʹdar Abdulovich Ibragimov and published by . This book was released on 1971 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Probability

Author : Rick Durrett
Publisher : Cambridge University Press
ISBN 13 : 113949113X
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Probability by : Rick Durrett

Download or read book Probability written by Rick Durrett and published by Cambridge University Press. This book was released on 2010-08-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

High-Dimensional Probability

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108244548
Total Pages : 299 pages
Book Rating : 4.1/5 (82 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression.

A History of the Central Limit Theorem

Author : Hans Fischer
Publisher : Springer Science & Business Media
ISBN 13 : 0387878572
Total Pages : 415 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis A History of the Central Limit Theorem by : Hans Fischer

Download or read book A History of the Central Limit Theorem written by Hans Fischer and published by Springer Science & Business Media. This book was released on 2010-10-08 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Limit Theorems for Multi-Indexed Sums of Random Variables

Author : Oleg Klesov
Publisher : Springer
ISBN 13 : 3662443880
Total Pages : 495 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Limit Theorems for Multi-Indexed Sums of Random Variables by : Oleg Klesov

Download or read book Limit Theorems for Multi-Indexed Sums of Random Variables written by Oleg Klesov and published by Springer. This book was released on 2014-10-13 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who work on limit theorems in probability theory, the statistical analysis of random fields, as well as in the field of random sets or stochastic geometry. The central topic is also important for statistical theory, developing statistical inferences for random fields, and also has applications to the sciences, including physics and chemistry.

A Course in Probability Theory

Author : Kai Lai Chung
Publisher : Academic Press
ISBN 13 : 0080570402
Total Pages : 381 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis A Course in Probability Theory by : Kai Lai Chung

Download or read book A Course in Probability Theory written by Kai Lai Chung and published by Academic Press. This book was released on 2014-06-28 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains about 500 exercises consisting mostly of special cases and examples, second thoughts and alternative arguments, natural extensions, and some novel departures. With a few obvious exceptions they are neither profound nor trivial, and hints and comments are appended to many of them. If they tend to be somewhat inbred, at least they are relevant to the text and should help in its digestion. As a bold venture I have marked a few of them with a * to indicate a "must", although no rigid standard of selection has been used. Some of these are needed in the book, but in any case the reader's study of the text will be more complete after he has tried at least those problems.

Univariate Stable Distributions

Author : John P. Nolan
Publisher : Springer Nature
ISBN 13 : 3030529150
Total Pages : 342 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Univariate Stable Distributions by : John P. Nolan

Download or read book Univariate Stable Distributions written by John P. Nolan and published by Springer Nature. This book was released on 2020-09-13 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios. Beginning with an introductory chapter that explains key ideas about stable laws, readers will be prepared for the more advanced topics that appear later. The following chapters present the theory of stable distributions, a wide range of applications, and statistical methods, with the final chapters focusing on regression, signal processing, and related distributions. Each chapter ends with a number of carefully chosen exercises. Links to free software are included as well, where readers can put these methods into practice. Univariate Stable Distributions is ideal for advanced undergraduate or graduate students in mathematics, as well as many other fields, such as statistics, economics, engineering, physics, and more. It will also appeal to researchers in probability theory who seek an authoritative reference on stable distributions.