Probability Theory Random Processes And Mathematical Statistics
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| Author | : I︠U︡riĭ Anatolʹevich Rozanov |
| Publisher | : Springer |
| Total Pages | : 280 |
| Release | : 1995-10-31 |
| Genre | : Mathematics |
| ISBN | : |
The second part (Chapters 4-6) provides a foundation of stochastic analysis, gives information on basic models of random processes and tools to study them. Here a certain familiarity with elements of functional analysis is necessary. Important material is presented in the form of examples to keep readers involved. Audience: This is a concise textbook for a graduate level course, with carefully selected topics representing the most important areas of modern probability, random processes and statistics.
| Author | : A. A. Sveshnikov |
| Publisher | : Courier Corporation |
| Total Pages | : 516 |
| Release | : 2012-04-30 |
| Genre | : Mathematics |
| ISBN | : 0486137562 |
Approximately 1,000 problems — with answers and solutions included at the back of the book — illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.
| Author | : Hossein Pishro-Nik |
| Publisher | : |
| Total Pages | : 746 |
| Release | : 2014-08-15 |
| Genre | : Probabilities |
| ISBN | : 9780990637202 |
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.
| Author | : Leonid Koralov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 346 |
| Release | : 2007-08-10 |
| Genre | : Mathematics |
| ISBN | : 3540688293 |
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.
| Author | : Robert Shevilevich Lipt︠s︡er |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 428 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 9783540639282 |
"Written by two renowned experts in the field, the books under review contain a thorough and insightful treatment of the fundamental underpinnings of various aspects of stochastic processes as well as a wide range of applications. Providing clear exposition, deep mathematical results, and superb technical representation, they are masterpieces of the subject of stochastic analysis and nonlinear filtering....These books...will become classics." --SIAM REVIEW
| Author | : Hisashi Kobayashi |
| Publisher | : Cambridge University Press |
| Total Pages | : 813 |
| Release | : 2011-12-15 |
| Genre | : Technology & Engineering |
| ISBN | : 1139502611 |
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.
| Author | : John J. Shynk |
| Publisher | : John Wiley & Sons |
| Total Pages | : 850 |
| Release | : 2012-10-15 |
| Genre | : Computers |
| ISBN | : 1118393953 |
Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several appendices include related material on integration, important inequalities and identities, frequency-domain transforms, and linear algebra. These topics have been included so that the book is relatively self-contained. One appendix contains an extensive summary of 33 random variables and their properties such as moments, characteristic functions, and entropy. Unlike most books on probability, numerous figures have been included to clarify and expand upon important points. Over 600 illustrations and MATLAB plots have been designed to reinforce the material and illustrate the various characterizations and properties of random quantities. Sufficient statistics are covered in detail, as is their connection to parameter estimation techniques. These include classical Bayesian estimation and several optimality criteria: mean-square error, mean-absolute error, maximum likelihood, method of moments, and least squares. The last four chapters provide an introduction to several topics usually studied in subsequent engineering courses: communication systems and information theory; optimal filtering (Wiener and Kalman); adaptive filtering (FIR and IIR); and antenna beamforming, channel equalization, and direction finding. This material is available electronically at the companion website. Probability, Random Variables, and Random Processes is the only textbook on probability for engineers that includes relevant background material, provides extensive summaries of key results, and extends various statistical techniques to a range of applications in signal processing.
| Author | : V. S. Pugachev |
| Publisher | : Elsevier |
| Total Pages | : 469 |
| Release | : 2014-06-28 |
| Genre | : Mathematics |
| ISBN | : 1483190501 |
Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables. The book underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vectors and their distributions, including conditional distributions of projections of a random vector, conditional numerical characteristics, and information contained in random variables. The book elaborates on the functions of random variables and estimation of parameters of distributions. Topics include frequency as a probability estimate, estimation of statistical characteristics, estimation of the expectation and covariance matrix of a random vector, and testing the hypotheses on the parameters of distributions. The text then takes a look at estimator theory and estimation of distributions. The book is a vital source of data for students, engineers, postgraduates of applied mathematics, and other institutes of higher technical education.
| Author | : Eugene Lukacs |
| Publisher | : Academic Press |
| Total Pages | : 255 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483269205 |
Probability and Mathematical Statistics: An Introduction provides a well-balanced first introduction to probability theory and mathematical statistics. This book is organized into two sections encompassing nine chapters. The first part deals with the concept and elementary properties of probability space, and random variables and their probability distributions. This part also considers the principles of limit theorems, the distribution of random variables, and the so-called student's distribution. The second part explores pertinent topics in mathematical statistics, including the concept of sampling, estimation, and hypotheses testing. This book is intended primarily for undergraduate statistics students.
| Author | : V.V. Buldygin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 314 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 9401716870 |
It is well known that contemporary mathematics includes many disci plines. Among them the most important are: set theory, algebra, topology, geometry, functional analysis, probability theory, the theory of differential equations and some others. Furthermore, every mathematical discipline consists of several large sections in which specific problems are investigated and the corresponding technique is developed. For example, in general topology we have the following extensive chap ters: the theory of compact extensions of topological spaces, the theory of continuous mappings, cardinal-valued characteristics of topological spaces, the theory of set-valued (multi-valued) mappings, etc. Modern algebra is featured by the following domains: linear algebra, group theory, the theory of rings, universal algebras, lattice theory, category theory, and so on. Concerning modern probability theory, we can easily see that the clas sification of its domains is much more extensive: measure theory on ab stract spaces, Borel and cylindrical measures in infinite-dimensional vector spaces, classical limit theorems, ergodic theory, general stochastic processes, Markov processes, stochastical equations, mathematical statistics, informa tion theory and many others.
