Download or read book Stationary Stochastic Processes written by Georg Lindgren and published by CRC Press. This book was released on 2012-10-01 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended for a second course in stationary processes, Stationary Stochastic Processes: Theory and Applications presents the theory behind the field’s widely scattered applications in engineering and science. In addition, it reviews sample function properties and spectral representations for stationary processes and fields, including a portion on stationary point processes. Features Presents and illustrates the fundamental correlation and spectral methods for stochastic processes and random fields Explains how the basic theory is used in special applications like detection theory and signal processing, spatial statistics, and reliability Motivates mathematical theory from a statistical model-building viewpoint Introduces a selection of special topics, including extreme value theory, filter theory, long-range dependence, and point processes Provides more than 100 exercises with hints to solutions and selected full solutions This book covers key topics such as ergodicity, crossing problems, and extremes, and opens the doors to a selection of special topics, like extreme value theory, filter theory, long-range dependence, and point processes, and includes many exercises and examples to illustrate the theory. Precise in mathematical details without being pedantic, Stationary Stochastic Processes: Theory and Applications is for the student with some experience with stochastic processes and a desire for deeper understanding without getting bogged down in abstract mathematics.
Download or read book Stationary Stochastic Processes for Scientists and Engineers written by Georg Lindgren and published by CRC Press. This book was released on 2013-10-11 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for a one-semester course, this text teaches students how to use stochastic processes efficiently. Carefully balancing mathematical rigor and ease of exposition, the book provides students with a sufficient understanding of the theory and a practical appreciation of how it is used in real-life situations. Special emphasis is on the interpretation of various statistical models and concepts as well as the types of questions statistical analysis can answer. To enable hands-on practice, MATLAB code is available online.
Download or read book Stationary Processes and Discrete Parameter Markov Processes written by Rabi Bhattacharya and published by Springer Nature. This book was released on 2022-12-01 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. After recapping the essentials from Fourier analysis, the book begins with an introduction to the spectral representation of a stationary process. Topics in ergodic theory follow, including Birkhoff’s Ergodic Theorem and an introduction to dynamical systems. From here, the Markov property is assumed and the theory of discrete parameter Markov processes is explored on a general state space. Chapters cover a variety of topics, including birth–death chains, hitting probabilities and absorption, the representation of Markov processes as iterates of random maps, and large deviation theory for Markov processes. A chapter on geometric rates of convergence to equilibrium includes a splitting condition that captures the recurrence structure of certain iterated maps in a novel way. A selection of special topics concludes the book, including applications of large deviation theory, the FKG inequalities, coupling methods, and the Kalman filter. Featuring many short chapters and a modular design, this textbook offers an in-depth study of stationary and discrete-time Markov processes. Students and instructors alike will appreciate the accessible, example-driven approach and engaging exercises throughout. A single, graduate-level course in probability is assumed.
Download or read book Stationary Processes and Prediction Theory AM 44 Volume 44 written by Harry Furstenberg and published by Princeton University Press. This book was released on 2016-03-02 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stationary and Related Stochastic Processes written by Harald Cramér and published by Courier Corporation. This book was released on 2013-01-15 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text offers a comprehensive account of the general theory of stationary processes and develops the foundations of the general theory of stochastic processes, examines processes with a continuous-time parameter, more. 1967 edition.
Download or read book Stationary Stochastic Processes MN 8 written by Takeyuki Hida and published by Princeton University Press. This book was released on 2015-03-08 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Encompassing both introductory and more advanced research material, these notes deal with the author's contributions to stochastic processes and focus on Brownian motion processes and its derivative white noise. Originally published in 1970. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Noncommutative Stationary Processes written by Rolf Gohm and published by Springer Science & Business Media. This book was released on 2004 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stationary Random Processes Associated with Point Processes written by Tomasz Rolski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this set of notes we study a notion of a random process assoc- ted with a point process. The presented theory was inSpired by q- ueing problems. However it seems to be of interest in other branches of applied probability, as for example reliability or dam theory. Using developed tools, we work out known, aswell as new results from queueing or dam theory. Particularly queues which cannot be treated by standard techniques serve as illustrations of the theory. In Chapter 1 the preliminaries are given. We acquaint the reader with the main ideas of these notes, introduce some useful notations, concepts and abbreviations. He also recall basic facts from ergodic theory, an important mathematical tool employed in these notes. Finally some basic notions from queues are reviewed. Chapter 2 deals with discrete time theory. It serves two purposes. The first one is to let the reader get acquainted with the main lines of the theory needed in continuous time without being bothered by tech nical details. However the discrete time theory also seems to be of interest itself. There are examples which have no counte~ in continuous time. Chapter 3 deals with continuous time theory. It also contains many basic results from queueing or dam theory. Three applications of the continuous time theory are given in Chapter 4. We show how to use the theory in order to get some useful bounds for the stationary distribution of a random process.
Download or read book Stationary Processes and Prediction Theory written by Harry Furstenberg and published by Princeton University Press. This book was released on 1960-08-21 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stationary Random Processes written by I︠U︡riĭ Anatolʹevich Rozanov and published by . This book was released on 1967 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stationary Sequences and Random Fields written by Murray Rosenblatt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has a dual purpose. One of these is to present material which selec tively will be appropriate for a quarter or semester course in time series analysis and which will cover both the finite parameter and spectral approach. The second object is the presentation of topics of current research interest and some open questions. I mention these now. In particular, there is a discussion in Chapter III of the types of limit theorems that will imply asymptotic nor mality for covariance estimates and smoothings of the periodogram. This dis cussion allows one to get results on the asymptotic distribution of finite para meter estimates that are broader than those usually given in the literature in Chapter IV. A derivation of the asymptotic distribution for spectral (second order) estimates is given under an assumption of strong mixing in Chapter V. A discussion of higher order cumulant spectra and their large sample properties under appropriate moment conditions follows in Chapter VI. Probability density, conditional probability density and regression estimates are considered in Chapter VII under conditions of short range dependence. Chapter VIII deals with a number of topics. At first estimates for the structure function of a large class of non-Gaussian linear processes are constructed. One can determine much more about this structure or transfer function in the non-Gaussian case than one can for Gaussian processes. In particular, one can determine almost all the phase information.
Download or read book Advances in Condition Monitoring of Machinery in Non Stationary Operations written by Anna Timofiejczuk and published by Springer. This book was released on 2017-09-20 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with a snapshot of recent methods for non-stationary vibration analysis of machinery. It covers a broad range of advanced techniques in condition monitoring of machinery, such as mathematical models, signal processing and pattern recognition methods and artificial intelligence methods, and their practical applications to the analysis of nonstationarities. Each chapter, accepted after a rigorous peer-review process, reports on a selected, original piece of work presented and discussed at the International Conference on Condition Monitoring of Machinery in Non-Stationary Operations, CMMNO’2016, held on September 12 – 16, 2016, in Gliwice, Poland. The contributions cover advances in both theory and practice in a variety of subfields, such as: smart materials and structures; fluid-structure interaction; structural acoustics as well as computational vibro-acoustics and numerical methods. Further topics include: engines control, noise identification, robust design, flow-induced vibration and many others. By presenting state-of-the-art in predictive maintenance solutions and discussing important industrial issues the book offers a valuable resource to both academics and professionals and is expected to facilitate communication and collaboration between the two groups.
Download or read book Stochastic Processes and Related Topics written by Stamatis Cambanis and published by Springer Science & Business Media. This book was released on 1998 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Representation and Structure of Stable Self-Similar Processes.- Three Elementary Proofs of the Central Limit Theorem with Applications to Random Sums.- Almost Everywhere Convergence and SLLN Under Rearrangements.- Sufficient Conditions for the Existence of Conditional Moments of Stable Random Variables.- How Heavy are the Tails of a Stationary HARCH(k) Process? A Study of the Moments.- Use of Stochastic Comparisons in Communication Networks.- On the Conditional Variance-Covariance of Stable Random Vectors, II.- Interacting Particle Approximation for Fractal Burgers Equation.- Optimal Transformations for Prediction in Continuous-Time Stochastic Processes.- Algebraic Methods Toward Higher-Order Probability Inequalities.- Comparison and Deviation from a Representation Formula.- Components of the Strong Markov Property.- The Russian Options.- Cycle Representations of Markov Processes: An Application to Rotational Partitions.- On Extreme Values in Stationary Random Fields.- Norming Operators for Operator-Self-Similar Processes.- Multivariate Probability Density and Regression Functions Estimation of Continuous-time Stationary Processes from Discrete-time Data.- Tracing the Path of a Wright-Fisher Process with One-way Mutation in the Case of a Large Deviation.- A Distribution Inequality for Martingales with Bounded Symmetric Differences.- Moment Comparison of Multilinear Forms in Stable and Semistable Random Variables with Application to Semistable Multiple Integrals.- Global Dependency Measure for Sets of Random Elements: "The Italian Problem" and Some Consequences.
Download or read book Modelling Longitudinal and Spatially Correlated Data written by Timothy G. Gregoire and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Correlated data arise in numerous contexts across a wide spectrum of subject-matter disciplines. Modeling such data present special challenges and opportunities that have received increasing scrutiny by the statistical community in recent years. In October 1996 a group of 210 statisticians and other scientists assembled on the small island of Nantucket, U. S. A. , to present and discuss new developments relating to Modelling Longitudinal and Spatially Correlated Data: Methods, Applications, and Future Direc tions. Its purpose was to provide a cross-disciplinary forum to explore the commonalities and meaningful differences in the source and treatment of such data. This volume is a compilation of some of the important invited and volunteered presentations made during that conference. The three days and evenings of oral and displayed presentations were arranged into six broad thematic areas. The session themes, the invited speakers and the topics they addressed were as follows: • Generalized Linear Models: Peter McCullagh-"Residual Likelihood in Linear and Generalized Linear Models" • Longitudinal Data Analysis: Nan Laird-"Using the General Linear Mixed Model to Analyze Unbalanced Repeated Measures and Longi tudinal Data" • Spatio---Temporal Processes: David R. Brillinger-"Statistical Analy sis of the Tracks of Moving Particles" • Spatial Data Analysis: Noel A. Cressie-"Statistical Models for Lat tice Data" • Modelling Messy Data: Raymond J. Carroll-"Some Results on Gen eralized Linear Mixed Models with Measurement Error in Covariates" • Future Directions: Peter J.
Download or read book Handbook of Environmental and Ecological Statistics written by Alan E. Gelfand and published by CRC Press. This book was released on 2019-01-15 with total page 679 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook focuses on the enormous literature applying statistical methodology and modelling to environmental and ecological processes. The 21st century statistics community has become increasingly interdisciplinary, bringing a large collection of modern tools to all areas of application in environmental processes. In addition, the environmental community has substantially increased its scope of data collection including observational data, satellite-derived data, and computer model output. The resultant impact in this latter community has been substantial; no longer are simple regression and analysis of variance methods adequate. The contribution of this handbook is to assemble a state-of-the-art view of this interface. Features: An internationally regarded editorial team. A distinguished collection of contributors. A thoroughly contemporary treatment of a substantial interdisciplinary interface. Written to engage both statisticians as well as quantitative environmental researchers. 34 chapters covering methodology, ecological processes, environmental exposure, and statistical methods in climate science.
Download or read book Gaussian Random Processes written by I.A. Ibragimov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes.
Download or read book Stationary Marked Point Processes written by Karl Sigman and published by Chapman and Hall/CRC. This book was released on 1995-05-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking an applied point of view, this book provides an accessible introduction to the theory of stationary random marked point processes on the non-negative real line. The reader will be able to gain an intuitive understanding of stationary marked point processes and be able to apply the theory to stochastic modeling. The emphasis is on time averages and asymptotic stationarity. Proofs of the main results are given using shift-coupling methods and measure theory is kept to a minimum. Examples and exercises are given involving explicit construction of time and event stationary versions, using the 'inspection paradox' as an intuitive guide. The Rate Conservation Law is given and used in applications to queueing theory. The prerequisites are a background in probability theory and stochastic processes up to conditional expectation.
