Download or read book Conditional Probability Distribution in the Wide Sense written by Lester E. Dubins and published by . This book was released on 1957 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Processes written by J. L. Doob and published by Wiley-Interscience. This book was released on 1990-01-25 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of stochastic processes has developed so much in the last twenty years that the need for a systematic account of the subject has been felt, particularly by students and instructors of probability. This book fills that need. While even elementary definitions and theorems are stated in detail, this is not recommended as a first text in probability and there has been no compromise with the mathematics of probability. Since readers complained that omission of certain mathematical detail increased the obscurity of the subject, the text contains various mathematical points that might otherwise seem extraneous. A supplement includes a treatment of the various aspects of measure theory. A chapter on the specialized problem of prediction theory has also been included and references to the literature and historical remarks have been collected in the Appendix.
Download or read book Probability Random Processes and Statistical Analysis written by Hisashi Kobayashi and published by Cambridge University Press. This book was released on 2011-12-15 with total page 813 pages. Available in PDF, EPUB and Kindle. Book excerpt: Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.
Download or read book Chance Choice written by Kai Lai Chung and published by World Scientific. This book was released on 2004 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book begins with a historical essay entitled OC Will the Sun Rise Again?OCO and ends with a general address entitled OC Mathematics and ApplicationsOCO. The articles cover an interesting range of topics: combinatoric probabilities, classical limit theorems, Markov chains and processes, potential theory, Brownian motion, SchrAdingerOCoFeynman problems, etc. They include many addresses presented at international conferences and special seminars, as well as memorials to and reminiscences of prominent contemporary mathematicians and reviews of their works. Rare old photos of many of them enliven the book. Contents: On Mutually Favorable Events; On Fluctuations in Coin-Tossing; On a Stochastic Approximation Method; On the Martin Boundary for Markov Chains; A Cluster of Great Formulas; Probabilistic Methods in Markov Chains; Markov Processes with Infinities; Probability Methods in Potential Theory; Plya''s Work in Probability; Probability and Doob; In Memory of L(r)vy and Fr(r)chet; and other papers. Readership: Graduate students, teachers and researchers in probability and statistics."
Download or read book A Course in Probability Theory written by Kai Lai Chung and published by Academic Press. This book was released on 2001 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses. While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication.
Download or read book Markov Chains with Stationary Transition Probabilities written by Kai Lai Chung and published by Springer. This book was released on 2013-03-08 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Markov chains, although a special case of Markov processes, is here developed for its own sake and presented on its own merits. In general, the hypothesis of a denumerable state space, which is the defining hypothesis of what we call a "chain" here, generates more clear-cut questions and demands more precise and definitive an swers. For example, the principal limit theorem (§§ 1. 6, II. 10), still the object of research for general Markov processes, is here in its neat final form; and the strong Markov property (§ 11. 9) is here always applicable. While probability theory has advanced far enough that a degree of sophistication is needed even in the limited context of this book, it is still possible here to keep the proportion of definitions to theorems relatively low. . From the standpoint of the general theory of stochastic processes, a continuous parameter Markov chain appears to be the first essentially discontinuous process that has been studied in some detail. It is common that the sample functions of such a chain have discontinuities worse than jumps, and these baser discontinuities play a central role in the theory, of which the mystery remains to be completely unraveled. In this connection the basic concepts of separability and measurability, which are usually applied only at an early stage of the discussion to establish a certain smoothness of the sample functions, are here applied constantly as indispensable tools.
Download or read book Probability written by A.N. Shiryaev and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is based on a three-semester course of lectures given by the author in recent years in the Mechanics-Mathematics Faculty of Moscow State University and issued, in part, in mimeographed form under the title Probability, Statistics, Stochastic Processes, I, II by the Moscow State University Press. We follow tradition by devoting the first part of the course (roughly one semester) to the elementary theory of probability (Chapter I). This begins with the construction of probabilistic models with finitely many outcomes and introduces such fundamental probabilistic concepts as sample spaces, events, probability, independence, random variables, expectation, corre lation, conditional probabilities, and so on. Many probabilistic and statistical regularities are effectively illustrated even by the simplest random walk generated by Bernoulli trials. In this connection we study both classical results (law of large numbers, local and integral De Moivre and Laplace theorems) and more modern results (for example, the arc sine law). The first chapter concludes with a discussion of dependent random vari ables generated by martingales and by Markov chains.
Download or read book Introduction to Probability written by George G. Roussas and published by Academic Press. This book was released on 2013-11-27 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Probability, Second Edition, discusses probability theory in a mathematically rigorous, yet accessible way. This one-semester basic probability textbook explains important concepts of probability while providing useful exercises and examples of real world applications for students to consider. This edition demonstrates the applicability of probability to many human activities with examples and illustrations. After introducing fundamental probability concepts, the book proceeds to topics including conditional probability and independence; numerical characteristics of a random variable; special distributions; joint probability density function of two random variables and related quantities; joint moment generating function, covariance and correlation coefficient of two random variables; transformation of random variables; the Weak Law of Large Numbers; the Central Limit Theorem; and statistical inference. Each section provides relevant proofs, followed by exercises and useful hints. Answers to even-numbered exercises are given and detailed answers to all exercises are available to instructors on the book companion site. This book will be of interest to upper level undergraduate students and graduate level students in statistics, mathematics, engineering, computer science, operations research, actuarial science, biological sciences, economics, physics, and some of the social sciences. - Demonstrates the applicability of probability to many human activities with examples and illustrations - Discusses probability theory in a mathematically rigorous, yet accessible way - Each section provides relevant proofs, and is followed by exercises and useful hints - Answers to even-numbered exercises are provided and detailed answers to all exercises are available to instructors on the book companion site
Download or read book AFOSR written by United States. Air Force. Office of Scientific Research and published by . This book was released on 1957 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Stochastic Analysis written by M. M. Rao and published by Elsevier. This book was released on 2014-07-10 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Stochastic Analysis deals with the foundations of the theory of Kolmogorov and Bochner and its impact on the growth of stochastic analysis. Topics covered range from conditional expectations and probabilities to projective and direct limits, as well as martingales and likelihood ratios. Abstract martingales and their applications are also discussed. Comprised of five chapters, this volume begins with an overview of the basic Kolmogorov-Bochner theorem, followed by a discussion on conditional expectations and probabilities containing several characterizations of operators and measures. The applications of these conditional expectations and probabilities to Reynolds operators are also considered. The reader is then introduced to projective limits, direct limits, and a generalized Kolmogorov existence theorem, along with infinite product conditional probability measures. The book also considers martingales and their applications to likelihood ratios before concluding with a description of abstract martingales and their applications to convergence and harmonic analysis, as well as their relation to ergodic theory. This monograph should be of considerable interest to researchers and graduate students working in stochastic analysis.
Download or read book Operations Research unclassified Title written by Defense Documentation Center (U.S.) and published by . This book was released on 1962 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Probability with STEM Applications written by Matthew A. Carlton and published by John Wiley & Sons. This book was released on 2020-12-22 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability with STEM Applications, Third Edition, is an accessible and well-balanced introduction to post-calculus applied probability. Integrating foundational mathematical theory and the application of probability in the real world, this leading textbook engages students with unique problem scenarios and more than 1100 exercises of varying levels of difficulty. The text uses a hands-on, software-oriented approach to the subject of probability. MATLAB and R examples and exercises — complemented by computer code that enables students to create their own simulations — demonstrate the importance of software to solve problems that cannot be obtained analytically. Revised and updated throughout, the textbook covers basic properties of probability, random variables and their probability distributions, a brief introduction to statistical inference, Markov chains, stochastic processes, and signal processing. This new edition is the perfect text for a one-semester course and contains enough additional material for an entire academic year. The blending of theory and application will appeal not only to mathematics and statistics majors but also to engineering students, and quantitative business and social science majors. New to this Edition: Offered as a traditional textbook and in enhanced ePub format, containing problems with show/hide solutions and interactive applets and illustrations Revised and expanded chapters on conditional probability and independence, families of continuous distributions, and Markov chains New problems and updated problem sets throughout Features: Introduces basic theoretical knowledge in the first seven chapters, serving as a self-contained textbook of roughly 650 problems Provides numerous up-to-date examples and problems in R and MATLAB Discusses examples from recent journal articles, classic problems, and various practical applications Includes a chapter specifically designed for electrical and computer engineers, suitable for a one-term class on random signals and noise Contains appendices of statistical tables, background mathematics, and important probability distributions
Download or read book Introduction to the Theory of Random Processes written by Iosif Il?ich Gikhman and published by Courier Corporation. This book was released on 1996-01-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rigorous exposition suitable for elementary instruction. Covers measure theory, axiomatization of probability theory, processes with independent increments, Markov processes and limit theorems for random processes, more. A wealth of results, ideas, and techniques distinguish this text. Introduction. Bibliography. 1969 edition.
Download or read book Intermediate Mathematical Statistics written by G.P. Beaumont and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers those basic topics which usually form the core of intermediate courses in statistical theory; it is largely about estima tion and hypothesis testing. It is intended for undergraduates following courses in statistics but is also suitable preparatory read ing for some postgraduate courses. It is assumed that the reader has completed an introductory course which covered probability, random variables, moments and the sampling distributions. The level of mathematics required does not go beyond first year calculus. In case the reader has not acquired much facility in handling matrices, the results in least squares estimation are first obtained directly and then given an (optional) matrix formulation. If techniques for changing from one set of variables to another have not been met, then the appendix on these topics should be studied first. The same appendix contains essential discussion of the order statistics which are frequently used for illustrative purposes. Introductory courses usually include the elements of hypothesis testing and of point and interval estimation though the treatment must perforce become rather thin since at that stage it is difficult to provide adequate justifications for some procedures-plausible though they may seem. This text discusses these important topics in considerable detail, starting from scratch. The level is nowhere advanced and proofs of asymptotic results are omitted. Methods deriving from the Bayesian point of view are gradually introduced and alternate with the more usual techniques.
Download or read book Probability with Applications in Engineering Science and Technology written by Matthew A. Carlton and published by Springer. This book was released on 2017-03-30 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This updated and revised first-course textbook in applied probability provides a contemporary and lively post-calculus introduction to the subject of probability. The exposition reflects a desirable balance between fundamental theory and many applications involving a broad range of real problem scenarios. It is intended to appeal to a wide audience, including mathematics and statistics majors, prospective engineers and scientists, and those business and social science majors interested in the quantitative aspects of their disciplines. The textbook contains enough material for a year-long course, though many instructors will use it for a single term (one semester or one quarter). As such, three course syllabi with expanded course outlines are now available for download on the book’s page on the Springer website. A one-term course would cover material in the core chapters (1-4), supplemented by selections from one or more of the remaining chapters on statistical inference (Ch. 5), Markov chains (Ch. 6), stochastic processes (Ch. 7), and signal processing (Ch. 8—available exclusively online and specifically designed for electrical and computer engineers, making the book suitable for a one-term class on random signals and noise). For a year-long course, core chapters (1-4) are accessible to those who have taken a year of univariate differential and integral calculus; matrix algebra, multivariate calculus, and engineering mathematics are needed for the latter, more advanced chapters. At the heart of the textbook’s pedagogy are 1,100 applied exercises, ranging from straightforward to reasonably challenging, roughly 700 exercises in the first four “core” chapters alone—a self-contained textbook of problems introducing basic theoretical knowledge necessary for solving problems and illustrating how to solve the problems at hand – in R and MATLAB, including code so that students can create simulations. New to this edition • Updated and re-worked Recommended Coverage for instructors, detailing which courses should use the textbook and how to utilize different sections for various objectives and time constraints • Extended and revised instructions and solutions to problem sets • Overhaul of Section 7.7 on continuous-time Markov chains • Supplementary materials include three sample syllabi and updated solutions manuals for both instructors and students
Download or read book ANALOG COMMUNICATION written by TOMAR, GEETAM SINGH and published by PHI Learning Pvt. Ltd.. This book was released on 2016-02-25 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book carries a holistic approach on the analog communication, with all the basic concepts pertaining to the subject described in it. The text provides an incisive insight into the subject via simple, elegant and explicit presentation. Organised in ten chapters, the book dexterously assimilates the various terms and techniques used in analog communication to enhance a broader understanding of the concepts and their applications. Commencing with the basic introduction, the book goes on to provide description on analog amplitude modulation, single sideband modulation, analog angle modulation, pulse modulation digital transmission of analog signals and multiplexing. Finally, it discusses about noise, random signal and processes, information theory and coding, and communication detectors and filters. The background of each topic in the book is prepared sensibly by providing suitable illustrations, numerical examples, detailed explanation of each step given, thereby making the understanding of complicated derivations easier. This well-structured book is specifically written for the undergraduate students of electronics and communication engineering, and postgraduate students of electronics.
