Download A Graduate Course In Probability full books in PDF, epub, and Kindle. Read online A Graduate Course In Probability ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
This textbook on the theory of probability 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 explanations of the three main subjects in probability: 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.
Book Synopsis Probability: A Graduate Course by : Allan Gut
Download or read book Probability: A Graduate Course written by Allan Gut and published by Springer Science & Business Media. This book was released on 2006-03-16 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on the theory of probability 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 explanations of the three main subjects in probability: 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.
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.
Book Synopsis A Graduate Course in Probability by : Howard G. Tucker
Download or read book A Graduate Course in Probability written by Howard G. Tucker and published by Academic Press. This book was released on 2014-06-27 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
The purpose of this book is to provide the reader with a solid background and understanding of the basic results and methods in probability the ory before entering into more advanced courses (in probability and/or statistics). The presentation is fairly thorough and detailed with many solved examples. Several examples are solved with different methods in order to illustrate their different levels of sophistication, their pros, and their cons. The motivation for this style of exposition is that experi ence has proved that the hard part in courses of this kind usually in the application of the results and methods; to know how, when, and where to apply what; and then, technically, to solve a given problem once one knows how to proceed. Exercises are spread out along the way, and every chapter ends with a large selection of problems. Chapters I through VI focus on some central areas of what might be called pure probability theory: multivariate random variables, condi tioning, transforms, order variables, the multivariate normal distribution, and convergence. A final chapter is devoted to the Poisson process be cause of its fundamental role in the theory of stochastic processes, but also because it provides an excellent application of the results and meth ods acquired earlier in the book. As an extra bonus, several facts about this process, which are frequently more or less taken for granted, are thereby properly verified.
Book Synopsis An Intermediate Course in Probability by : Allan Gut
Download or read book An Intermediate Course in Probability written by Allan Gut and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide the reader with a solid background and understanding of the basic results and methods in probability the ory before entering into more advanced courses (in probability and/or statistics). The presentation is fairly thorough and detailed with many solved examples. Several examples are solved with different methods in order to illustrate their different levels of sophistication, their pros, and their cons. The motivation for this style of exposition is that experi ence has proved that the hard part in courses of this kind usually in the application of the results and methods; to know how, when, and where to apply what; and then, technically, to solve a given problem once one knows how to proceed. Exercises are spread out along the way, and every chapter ends with a large selection of problems. Chapters I through VI focus on some central areas of what might be called pure probability theory: multivariate random variables, condi tioning, transforms, order variables, the multivariate normal distribution, and convergence. A final chapter is devoted to the Poisson process be cause of its fundamental role in the theory of stochastic processes, but also because it provides an excellent application of the results and meth ods acquired earlier in the book. As an extra bonus, several facts about this process, which are frequently more or less taken for granted, are thereby properly verified.
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.
Book Synopsis Mathematics of Probability by : Daniel W. Stroock
Download or read book Mathematics of Probability written by Daniel W. Stroock and published by American Mathematical Soc.. This book was released on 2013-07-05 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded. General Markov dependent sequences and their convergence to equilibrium is the subject of an entirely new chapter. The introduction of conditional expectation and conditional probability very early in the text maintains the pedagogic innovation of the first edition; conditional expectation is illustrated in detail in the context of an expanded treatment of martingales, the Markov property, and the strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of large deviation and/or concentration inequalities ranging from those of Chebyshev, Cramer–Chernoff, Bahadur–Rao, to Hoeffding have been added, with illustrative comparisons of their use in practice. This also includes a treatment of the Berry–Esseen error estimate in the central limit theorem. The authors assume mathematical maturity at a graduate level; otherwise the book is suitable for students with varying levels of background in analysis and measure theory. For the reader who needs refreshers, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference. Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored numerous books, including a series of four upcoming graduate textbooks in stochastic processes with applications.
Book Synopsis A Basic Course in Probability Theory by : Rabi Bhattacharya
Download or read book A Basic Course in Probability Theory written by Rabi Bhattacharya and published by Springer. This book was released on 2017-02-13 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text develops the necessary background in probability theory underlying diverse treatments of stochastic processes and their wide-ranging applications. In this second edition, the text has been reorganized for didactic purposes, new exercises have been added and basic theory has been expanded. General Markov dependent sequences and their convergence to equilibrium is the subject of an entirely new chapter. The introduction of conditional expectation and conditional probability very early in the text maintains the pedagogic innovation of the first edition; conditional expectation is illustrated in detail in the context of an expanded treatment of martingales, the Markov property, and the strong Markov property. Weak convergence of probabilities on metric spaces and Brownian motion are two topics to highlight. A selection of large deviation and/or concentration inequalities ranging from those of Chebyshev, Cramer–Chernoff, Bahadur–Rao, to Hoeffding have been added, with illustrative comparisons of their use in practice. This also includes a treatment of the Berry–Esseen error estimate in the central limit theorem. The authors assume mathematical maturity at a graduate level; otherwise the book is suitable for students with varying levels of background in analysis and measure theory. For the reader who needs refreshers, theorems from analysis and measure theory used in the main text are provided in comprehensive appendices, along with their proofs, for ease of reference. Rabi Bhattacharya is Professor of Mathematics at the University of Arizona. Edward Waymire is Professor of Mathematics at Oregon State University. Both authors have co-authored numerous books, including a series of four upcoming graduate textbooks in stochastic processes with applications.
"Suitable for a graduate course in analytic probability, this text requires only a limited background in real analysis. Topics include probability spaces and distributions, stochastic independence, basic limiting options, strong limit theorems for independent random variables, central limit theorem, conditional expectation and Martingale theory, and an introduction to stochastic processes"--
Book Synopsis A Graduate Course in Probability by : Howard G. Tucker
Download or read book A Graduate Course in Probability written by Howard G. Tucker and published by Courier Corporation. This book was released on 2014-02-20 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Suitable for a graduate course in analytic probability, this text requires only a limited background in real analysis. Topics include probability spaces and distributions, stochastic independence, basic limiting options, strong limit theorems for independent random variables, central limit theorem, conditional expectation and Martingale theory, and an introduction to stochastic processes"--
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.
Book Synopsis Probability by : Davar Khoshnevisan
Download or read book Probability written by Davar Khoshnevisan and published by American Mathematical Soc.. This book was released on 2007 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
The use of the Black-Scholes model and formula is pervasive in financial markets. There are very few undergraduate textbooks available on the subject and, until now, almost none written by mathematicians. Based on a course given by the author, the goal of
Book Synopsis Probability Theory in Finance by : Seán Dineen
Download or read book Probability Theory in Finance written by Seán Dineen and published by American Mathematical Soc.. This book was released on 2013-05-22 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of the Black-Scholes model and formula is pervasive in financial markets. There are very few undergraduate textbooks available on the subject and, until now, almost none written by mathematicians. Based on a course given by the author, the goal of
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.
Book Synopsis Probability and Stochastics by : Erhan Çınlar
Download or read book Probability and Stochastics written by Erhan Çınlar and published by Springer Science & Business Media. This book was released on 2011-02-21 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
Book Synopsis Introduction to Probability by : David F. Anderson
Download or read book Introduction to Probability written by David F. Anderson and published by Cambridge University Press. This book was released on 2017-11-02 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.
