Probability A Graduate Course
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Probability
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Author : Allan Gut
language : en
Publisher: Springer Science & Business Media
Release Date : 2013
Probability written by Allan Gut 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 2013 with Mathematics categories.
Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by a thorough treatment of the three main subjects in probability theory: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including some new material as well as around a dozen new references.
Probability A Graduate Course
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Author : Allan Gut
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-16
Probability A Graduate Course written by Allan Gut 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 2006-03-16 with Mathematics categories.
"I know it's trivial, but I have forgotten why". This is a slightly exaggerated characterization of the unfortunate attitude of many mathematicians toward the surrounding world. The point of departure of this book is the opposite. This textbook on the theory of probability is aimed at graduate students, with the ideology that rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to chapters on inequalities, characteristic functions, convergence, followed by the three main subjects, the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The main feature of this book is the combination of rigor and detail. Instead of being sketchy and leaving lots of technicalities to be filled in by the reader or as easy exercises, a more solid foundation is obtained by providing more of those not so trivial matters and by integrating some of those not so simple exercises and problems into the body of text. Some results have been given more than one proof in order to illustrate the pros and cons of different approaches. On occasion we invite the reader to minor extensions, for which the proofs reduce to minor modifications of existing ones, with the aim of creating an atmosphere of a dialogue with the reader (instead of the more typical monologue), in order to put the reader in the position to approach any other text for which a solid probabilistic foundation is necessary. Allan Gut is a professor of Mathematical Statistics at Uppsala University, Uppsala, Sweden. He is the author of the Springer monograph "Stopped Random Walks" (1988), the Springer textbook "An Intermediate Course in Probability" (1995), and has published around 60 articles in probability theory. His interest in attracting amore general audience to the beautiful world of probability has been manifested in his Swedish popular science book Sant eller Sannolikt ("True or Probable"), Norstedts förlag (2002). From the reviews: "This is more substantial than the usual graduate course in probability; it contains many useful and interesting details that previously were scattered around the literature and gives clear evidence that the writer has a great deal of experience in the area." Short Book Reviews of the International Statistical Institute, December 2005 "...This book is a readable, comprehensive, and up-to-date introductory textbook to probability theory with emphasis on limit theorems for sums and extremes of random variables. The purchase is worth its price." Journal of the American Statistical Association, June 2006
A Graduate Course In Probability
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Author : Howard G. Tucker
language : en
Publisher: Academic Press
Release Date : 2014-06-27
A Graduate Course In Probability written by Howard G. Tucker and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-27 with Mathematics categories.
Probability and Mathematical Statistics: A Series of Monographs and Textbooks: A Graduate Course in Probability presents some of the basic theorems of analytic probability theory in a cohesive manner. This book discusses the probability spaces and distributions, stochastic independence, basic limiting operations, and strong limit theorems for independent random variables. The central limit theorem, conditional expectation and martingale theory, and Brownian motion are also elaborated. The prerequisite for this text is knowledge of real analysis or measure theory, particularly the Lebesgue dominated convergence theorem, Fubini's theorem, Radon-Nikodym theorem, Egorov's theorem, monotone convergence theorem, and theorem on unique extension of a sigma-finite measure from an algebra to the sigma-algebra generated by it. This publication is suitable for a one-year graduate course in probability given in a mathematics program and preferably for students in their second year of graduate work.
An Intermediate Course In Probability
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Author : Allan Gut
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-06
An Intermediate Course In Probability written by Allan Gut 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 2009-06-06 with Mathematics categories.
This is the only book that gives a rigorous and comprehensive treatment with lots of examples, exercises, remarks on this particular level between the standard first undergraduate course and the first graduate course based on measure theory. There is no competitor to this book. The book can be used in classrooms as well as for self-study.
Mathematics Of Probability
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Author : Daniel W. Stroock
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-07-05
Mathematics Of Probability written by Daniel W. Stroock 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 2013-07-05 with Mathematics categories.
This book covers the basics of modern probability theory. It begins with probability theory on finite and countable sample spaces and then passes from there to a concise course on measure theory, which is followed by some initial applications to probability theory, including independence and conditional expectations. The second half of the book deals with Gaussian random variables, with Markov chains, with a few continuous parameter processes, including Brownian motion, and, finally, with martingales, both discrete and continuous parameter ones. The book is a self-contained introduction to probability theory and the measure theory required to study it.
Probability
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Author : Davar Khoshnevisan
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Probability written by Davar Khoshnevisan 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 2007 with Mathematics categories.
This is a textbook for a one-semester graduate course in measure-theoretic probability theory, but with ample material to cover an ordinary year-long course at a more leisurely pace. Khoshnevisan's approach is to develop the ideas that are absolutely central to modern probability theory, and to showcase them by presenting their various applications. As a result, a few of the familiar topics are replaced by interesting non-standard ones. The topics range from undergraduate probability and classical limit theorems to Brownian motion and elements of stochastic calculus. Throughout, the reader will find many exciting applications of probability theory and probabilistic reasoning. There are numerous exercises, ranging from the routine to the very difficult. Each chapter concludes with historical notes.
Probability Theory With Applications
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Author : Malempati M. Rao
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-03
Probability Theory With Applications written by Malempati M. Rao 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 2006-06-03 with Mathematics categories.
This book is a revised and expanded edition of a successful graduate and reference text. The material in the book is designed for a standard graduate course on probability theory, including some important applications. This new edition contains a detailed treatment of the core area of probability, and both structural and limit results are presented in full detail. Compared to the first edition, the material and presentation are better highlighted with several (small and large) alterations made to each chapter. Key features of the book include: - Indicating the need for abstract theory even in applications and showing the inadequacy of existing results for certain apparently simple real-world problems - Attempting to deal with the existence problems for various classes of random families that figure in the main results of the subject - Providing a treatment of conditional expectations and of conditional probabilities that is more complete than in other existing textbooks Since this is a textbook, essentially all proofs are given in complete detail (even at the risk of repetition), and some key results are given multiple proofs when each argument has something to contribute.
A Modern Approach To Probability Theory
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Author : Bert E. Fristedt
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-12-23
A Modern Approach To Probability Theory written by Bert E. Fristedt 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 1996-12-23 with Mathematics categories.
Students and teachers of mathematics and related fields will find this book a comprehensive and modern approach to probability theory, providing the background and techniques to go from the beginning graduate level to the point of specialization in research areas of current interest. The book is designed for a two- or three-semester course, assuming only courses in undergraduate real analysis or rigorous advanced calculus, and some elementary linear algebra. A variety of applications—Bayesian statistics, financial mathematics, information theory, tomography, and signal processing—appear as threads to both enhance the understanding of the relevant mathematics and motivate students whose main interests are outside of pure areas.
Probability And Stochastics
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Author : Erhan Çınlar
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-21
Probability And Stochastics written by Erhan Çınlar 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 2011-02-21 with Mathematics categories.
This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form. The first four chapters are on probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes. Special attention is paid to Poisson random measures and their roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large number of varied examples and exercises. The book is based on the author’s lecture notes in courses offered over the years at Princeton University. These courses attracted graduate students from engineering, economics, physics, computer sciences, and mathematics. Erhan Cinlar has received many awards for excellence in teaching, including the President’s Award for Distinguished Teaching at Princeton University. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style.
Probability Essentials
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Author : Jean Jacod
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probability Essentials written by Jean Jacod 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.
We present here a one-semester course on Probability Theory. We also treat measure theory and Lebesgue integration, concentrating on those aspects which are especially germane to the study of Probability Theory. The book is intended to fill a current need: there are mathematically sophisticated stu dents and researchers (especially in Engineering, Economics, and Statistics) who need a proper grounding in Probability in order to pursue their primary interests. Many Probability texts available today are celebrations of Prob ability Theory, containing treatments of fascinating topics to be sure, but nevertheless they make it difficult to construct a lean one semester course that covers (what we believe are) the essential topics. Chapters 1-23 provide such a course. We have indulged ourselves a bit by including Chapters 24-28 which are highly optional, but which may prove useful to Economists and Electrical Engineers. This book had its origins in a course the second author gave in Perugia, Italy, in 1997; he used the samizdat "notes" of the first author, long used for courses at the University of Paris VI, augmenting them as needed. The result has been further tested at courses given at Purdue University. We thank the indulgence and patience of the students both in Perugia and in West Lafayette. We also thank our editor Catriona Byrne, as weil as Nick Bingham for many superb suggestions, an anonymaus referee for the same, and Judy Mitchell for her extraordinary typing skills. Jean Jacod, Paris Philip Protter, West Lafayette Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . .