Studies in the Theory of Random Processes PDF Download

Author: Anatoliĭ Vladimirovich Skorokhod
Publisher:
ISBN:
Category : Probabilities
Languages : en
Pages : 216

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Author: Nikolaĭ Vladimirovich Krylov
Publisher: American Mathematical Soc.
ISBN: 0821829858
Category : Mathematics
Languages : en
Pages : 245

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Book Description
This book concentrates on some general facts and ideas of the theory of stochastic processes. The topics include the Wiener process, stationary processes, infinitely divisible processes, and Ito stochastic equations. Basics of discrete time martingales are also presented and then used in one way or another throughout the book. Another common feature of the main body of the book is using stochastic integration with respect to random orthogonal measures. In particular, it is used forspectral representation of trajectories of stationary processes and for proving that Gaussian stationary processes with rational spectral densities are components of solutions to stochastic equations. In the case of infinitely divisible processes, stochastic integration allows for obtaining arepresentation of trajectories through jump measures. The Ito stochastic integral is also introduced as a particular case of stochastic integrals with respect to random orthogonal measures. Although it is not possible to cover even a noticeable portion of the topics listed above in a short book, it is hoped that after having followed the material presented here, the reader will have acquired a good understanding of what kind of results are available and what kind of techniques are used toobtain them. With more than 100 problems included, the book can serve as a text for an introductory course on stochastic processes or for independent study. Other works by this author published by the AMS include, Lectures on Elliptic and Parabolic Equations in Holder Spaces and Introduction to the Theoryof Diffusion Processes.

Author: A. V. Skorokhod
Publisher: Courier Corporation
ISBN: 0486781461
Category : Mathematics
Languages : en
Pages : 209

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Three-part treatment introduces basics plus theory of stochastic differential equations and various limit theorems connected with convergence of sequence of Markov chains to Markov process with continuous time. 1965 edition.

Author: Leonid Koralov
Publisher: Springer Science & Business Media
ISBN: 3540688293
Category : Mathematics
Languages : en
Pages : 346

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Book Description
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: Igor N. Kovalenko
Publisher: CRC Press
ISBN: 9780849328701
Category : Mathematics
Languages : en
Pages : 456

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Devising and investigating random processes that describe mathematical models of phenomena is a major aspect of probability theory applications. Stochastic methods have penetrated into an unimaginably wide scope of problems encountered by researchers who need stochastic methods to solve problems and further their studies. This handbook supplies the knowledge you need on the modern theory of random processes. Packed with methods, Models of Random Processes: A Handbook for Mathematicians and Engineers presents definitions and properties on such widespread processes as Poisson, Markov, semi-Markov, Gaussian, and branching processes, and on special processes such as cluster, self-exiting, double stochastic Poisson, Gauss-Poisson, and extremal processes occurring in a variety of different practical problems. The handbook is based on an axiomatic definition of probability space, with strict definitions and constructions of random processes. Emphasis is placed on the constructive definition of each class of random processes, so that a process is explicitly defined by a sequence of independent random variables and can easily be implemented into the modelling. Models of Random Processes: A Handbook for Mathematicians and Engineers will be useful to researchers, engineers, postgraduate students and teachers in the fields of mathematics, physics, engineering, operations research, system analysis, econometrics, and many others.

Author: Robert Shevilevich Lipt︠s︡er
Publisher: Springer Science & Business Media
ISBN: 9783540639282
Category : Mathematics
Languages : en
Pages : 428

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"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
ISBN: 1139502611
Category : Technology & Engineering
Languages : en
Pages : 813

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Book Description
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: Geoffrey Grimmett
Publisher: Oxford University Press
ISBN: 9780198572220
Category : Mathematics
Languages : en
Pages : 626

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Book Description
This textbook provides a wide-ranging and entertaining indroduction to probability and random processes and many of their practical applications. It includes many exercises and problems with solutions.

Author: Harry Furstenberg
Publisher: Princeton University Press
ISBN: 1400881609
Category : Mathematics
Languages : en
Pages : 300

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Book Description
A classic treatment of stationary processes and prediction theory from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.

Author: Iosif I. Gikhman
Publisher: Springer
ISBN: 3642619436
Category : Mathematics
Languages : en
Pages : 587

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Book Description
From the Reviews: "Gihman and Skorohod have done an excellent job of presenting the theory in its present state of rich imperfection." --D.W. Stroock, Bulletin of the American Mathematical Society, 1980