Author: Anatoliĭ Vladimirovich SkorokhodPublisher:
ISBN:
Category : Probabilities
Languages : en
Pages : 216
Book Description
Studies in the Theory of Random Processes
Author: Anatoliĭ Vladimirovich SkorokhodPublisher:
ISBN:
Category : Probabilities
Languages : en
Pages : 216
Book Description
Introduction to the Theory of Random Processes
Author: Nikolaĭ Vladimirovich KrylovPublisher: American Mathematical Soc.
ISBN: 0821829858
Category : Mathematics
Languages : en
Pages : 245
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.
Theory of Probability and Random Processes
Author: Leonid KoralovPublisher: Springer Science & Business Media
ISBN: 3540688293
Category : Mathematics
Languages : en
Pages : 346
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.
Models of Random Processes
Author: Igor N. KovalenkoPublisher: CRC Press
ISBN: 9780849328701
Category : Mathematics
Languages : en
Pages : 456
Book Description
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.
Probability, Stochastic Processes, and Queueing Theory
Author: Randolph NelsonPublisher: Springer Science & Business Media
ISBN: 1475724268
Category : Mathematics
Languages : en
Pages : 595
Book Description
We will occasionally footnote a portion of text with a "**,, to indicate Notes on the that this portion can be initially bypassed. The reasons for bypassing a Text portion of the text include: the subject is a special topic that will not be referenced later, the material can be skipped on first reading, or the level of mathematics is higher than the rest of the text. In cases where a topic is self-contained, we opt to collect the material into an appendix that can be read by students at their leisure. The material in the text cannot be fully assimilated until one makes it Notes on "their own" by applying the material to specific problems. Self-discovery Problems is the best teacher and although they are no substitute for an inquiring mind, problems that explore the subject from different viewpoints can often help the student to think about the material in a uniquely per sonal way. With this in mind, we have made problems an integral part of this work and have attempted to make them interesting as well as informative.
The Theory of Stochastic Processes
Author: Iosif I. GikhmanPublisher: Springer Science & Business Media
ISBN: 9783540202844
Category : Mathematics
Languages : en
Pages : 594
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 in Bulletin of the American Mathematical Society, 1980 "To call this work encyclopedic would not give an accurate picture of its content and style. Some parts read like a textbook, but others are more technical and contain relatively new results. ... The exposition is robust and explicit, as one has come to expect of the Russian tradition of mathematical writing. The set when completed will be an invaluable source of information and reference in this ever-expanding field" K.L. Chung in American Scientist, 1977 "..., the subject has grown enormously since 1953, and there will never be a true successor to Doob's book, but Gihman and Skorohod's three volumes will, I think, occupy a rather similar position as an invaluable tool of reference for all probability theorists. ... The dominant impression is of the authors' mastery of their material, and of their confident insight into its underlying structure. ..." J.F.C. Kingman in Bulletin of the London Mathematical Society, 1977
Statistics of Random Processes II
Author: Robert Shevilevich Lipt︠s︡erPublisher: Springer Science & Business Media
ISBN: 9783540639282
Category : Mathematics
Languages : en
Pages : 428
Book Description
"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
Probability and Random Processes
Author: Geoffrey GrimmettPublisher: Oxford University Press
ISBN: 9780198572220
Category : Mathematics
Languages : en
Pages : 626
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.
Probability, Random Processes, and Statistical Analysis
Author: Hisashi KobayashiPublisher: Cambridge University Press
ISBN: 1139502611
Category : Technology & Engineering
Languages : en
Pages : 813
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.
Thinking Probabilistically
Author: Ariel AmirPublisher: Cambridge University Press
ISBN: 1108479529
Category : Mathematics
Languages : en
Pages : 243
Book Description
An introductory text providing the reader with a thorough background to the rich world of applications of stochastic processes.