Probability Theory A Complete One Semester Course

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Probability Theory

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Author : Nikolai Dokuchaev
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015

Probability Theory written by Nikolai Dokuchaev and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.

This book provides a systematic, self-sufficient and yet short presentation of the mainstream topics on introductory Probability Theory with some selected topics from Mathematical Statistics. It is suitable for a 10- to 14-week course for second- or third-year undergraduate students in Science, Mathematics, Statistics, Finance, or Economics, who have completed some introductory course in Calculus. There is a sufficient number of problems and solutions to cover weekly tutorials.

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 . . . . . . . . . . . . . .

A Modern Introduction To Probability And Statistics

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Author : F.M. Dekking
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

A Modern Introduction To Probability And Statistics written by F.M. Dekking 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 2006-03-30 with Mathematics categories.

Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real life and using real data, the authors show how the fundamentals of probabilistic and statistical theories arise intuitively. A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to students. In addition there are over 350 exercises, half of which have answers, of which half have full solutions. A website gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to modern methods such as the bootstrap.

Introduction To Probability Statistics And Random Processes

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Author : Hossein Pishro-Nik
language : en
Publisher:
Release Date : 2014-08-15

Introduction To Probability Statistics And Random Processes written by Hossein Pishro-Nik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-15 with Probabilities categories.

The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities; limit theorems and convergence; introduction to Bayesian and classical statistics; random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion; simulation using MATLAB and R.

Theory Of Probability And Random Processes

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Author : Leonid Koralov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-10

Theory Of Probability And Random Processes written by Leonid Koralov 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 2007-08-10 with Mathematics categories.

A one-year course in probability theory and the theory of random processes, taught at Princeton University to undergraduate and graduate students, forms the core of this book. It provides a comprehensive and self-contained exposition of classical probability theory and the theory of random processes. The book includes detailed discussion of Lebesgue integration, Markov chains, random walks, laws of large numbers, limit theorems, and their relation to Renormalization Group theory. It also includes the theory of stationary random processes, martingales, generalized random processes, and Brownian motion.

Probability Theory

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Author : Alexandr A. Borovkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-22

Probability Theory written by Alexandr A. Borovkov 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 2013-06-22 with Mathematics categories.

This self-contained, comprehensive book tackles the principal problems and advanced questions of probability theory and random processes in 22 chapters, presented in a logical order but also suitable for dipping into. They include both classical and more recent results, such as large deviations theory, factorization identities, information theory, stochastic recursive sequences. The book is further distinguished by the inclusion of clear and illustrative proofs of the fundamental results that comprise many methodological improvements aimed at simplifying the arguments and making them more transparent. The importance of the Russian school in the development of probability theory has long been recognized. This book is the translation of the fifth edition of the highly successful Russian textbook. This edition includes a number of new sections, such as a new chapter on large deviation theory for random walks, which are of both theoretical and applied interest. The frequent references to Russian literature throughout this work lend a fresh dimension and make it an invaluable source of reference for Western researchers and advanced students in probability related subjects. Probability Theory will be of interest to both advanced undergraduate and graduate students studying probability theory and its applications. It can serve as a basis for several one-semester courses on probability theory and random processes as well as self-study.

An Introduction To Applied Probability

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Author : Ian F. Blake
language : en
Publisher:
Release Date : 1987

An Introduction To Applied Probability written by Ian F. Blake and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.

Designed for a curriculum that contains only 2 single one-semester course on probability. Covers the core of probability theory, considers sums of random variables, derives sampling distributions, and discusses the approximation of distributions. Includes nonstatistical and statistical applications such as hypothesis testing, confidence intervals, and regression analysis. Numerous worked examples throughout the text illustrate the material and each chapter concludes with a number of problems.

Measure Theory And Probability Theory

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Author : Krishna B. Athreya
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-27

Measure Theory And Probability Theory written by Krishna B. Athreya 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 2006-07-27 with Business & Economics categories.

This is a graduate level textbook on measure theory and probability theory. The book can be used as a text for a two semester sequence of courses in measure theory and probability theory, with an option to include supplemental material on stochastic processes and special topics. It is intended primarily for first year Ph.D. students in mathematics and statistics although mathematically advanced students from engineering and economics would also find the book useful. Prerequisites are kept to the minimal level of an understanding of basic real analysis concepts such as limits, continuity, differentiability, Riemann integration, and convergence of sequences and series. A review of this material is included in the appendix. The book starts with an informal introduction that provides some heuristics into the abstract concepts of measure and integration theory, which are then rigorously developed. The first part of the book can be used for a standard real analysis course for both mathematics and statistics Ph.D. students as it provides full coverage of topics such as the construction of Lebesgue-Stieltjes measures on real line and Euclidean spaces, the basic convergence theorems, L^p spaces, signed measures, Radon-Nikodym theorem, Lebesgue's decomposition theorem and the fundamental theorem of Lebesgue integration on R, product spaces and product measures, and Fubini-Tonelli theorems. It also provides an elementary introduction to Banach and Hilbert spaces, convolutions, Fourier series and Fourier and Plancherel transforms. Thus part I would be particularly useful for students in a typical Statistics Ph.D. program if a separate course on real analysis is not a standard requirement. Part II (chapters 6-13) provides full coverage of standard graduate level probability theory. It starts with Kolmogorov's probability model and Kolmogorov's existence theorem. It then treats thoroughly the laws of large numbers including renewal theory and ergodic theorems with applications and then weak convergence of probability distributions, characteristic functions, the Levy-Cramer continuity theorem and the central limit theorem as well as stable laws. It ends with conditional expectations and conditional probability, and an introduction to the theory of discrete time martingales. Part III (chapters 14-18) provides a modest coverage of discrete time Markov chains with countable and general state spaces, MCMC, continuous time discrete space jump Markov processes, Brownian motion, mixing sequences, bootstrap methods, and branching processes. It could be used for a topics/seminar course or as an introduction to stochastic processes. Krishna B. Athreya is a professor at the departments of mathematics and statistics and a Distinguished Professor in the College of Liberal Arts and Sciences at the Iowa State University. He has been a faculty member at University of Wisconsin, Madison; Indian Institute of Science, Bangalore; Cornell University; and has held visiting appointments in Scandinavia and Australia. He is a fellow of the Institute of Mathematical Statistics USA; a fellow of the Indian Academy of Sciences, Bangalore; an elected member of the International Statistical Institute; and serves on the editorial board of several journals in probability and statistics. Soumendra N. Lahiri is a professor at the department of statistics at the Iowa State University. He is a fellow of the Institute of Mathematical Statistics, a fellow of the American Statistical Association, and an elected member of the International Statistical Institute.

Applied Probability And Statistics

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Author : Mario Lefebvre
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-03

Applied Probability And Statistics written by Mario Lefebvre 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 2007-04-03 with Mathematics categories.

This book is based mainly on the lecture notes that I have been using since 1993 for a course on applied probability for engineers that I teach at the Ecole Polytechnique de Montreal. This course is given to electrical, computer and physics engineering students, and is normally taken during the second or third year of their curriculum. Therefore, we assume that the reader has acquired a basic knowledge of differential and integral calculus. The main objective of this textbook is to provide a reference that covers the topics that every student in pure or applied sciences, such as physics, computer science, engineering, etc., should learn in probability theory, in addition to the basic notions of stochastic processes and statistics. It is not easy to find a single work on all these topics that is both succinct and also accessible to non-mathematicians. Because the students, who for the most part have never taken a course on prob ability theory, must do a lot of exercises in order to master the material presented, I included a very large number of problems in the book, some of which are solved in detail. Most of the exercises proposed after each chapter are problems written es pecially for examinations over the years. They are not, in general, routine problems, like the ones found in numerous textbooks.

Probability

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Author : Rick Durrett
language : en
Publisher: Cambridge University Press
Release Date : 2010-08-30

Probability written by Rick Durrett and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-30 with Mathematics categories.

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.