Harmonizability, V-boundedness and Stationary Dilation of Stochastic Processes
Author | : Abolghassem G. Miamee |
Publisher | : |
Total Pages | : 52 |
Release | : 1977 |
Genre | : Stationary processes |
ISBN | : |
Download Harmonizability V Boundedness And Stationary Dilation Of Stochastic Processes full books in PDF, epub, and Kindle. Read online free Harmonizability V Boundedness And Stationary Dilation Of Stochastic Processes ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author | : Abolghassem G. Miamee |
Publisher | : |
Total Pages | : 52 |
Release | : 1977 |
Genre | : Stationary processes |
ISBN | : |
Author | : Yuichiro Kakihara |
Publisher | : World Scientific |
Total Pages | : 539 |
Release | : 2021-07-29 |
Genre | : Mathematics |
ISBN | : 9811211760 |
This is a development of the book entitled Multidimensional Second Order Stochastic Processes. It provides a research expository treatment of infinite-dimensional stationary and nonstationary stochastic processes or time series, based on Hilbert and Banach space-valued second order random variables. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes as well as the stationary class. A new type of the Radon-Nikodým derivative of a Banach space-valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes.Emphasis is on the use of functional analysis and harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Generalizations are made to consider Banach space-valued stochastic processes to include processes of pth order for p ≥ 1. Readers may find that the covariance kernel is always emphasized and reveals another aspect of stochastic processes.This book is intended not only for probabilists and statisticians, but also for functional analysts and communication engineers.
Author | : Yichir Kakihara |
Publisher | : World Scientific |
Total Pages | : 352 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9789810230005 |
A research-expository treatment of infinite-dimensional nonstationary stochastic processes (or time series) on a locally compact abelian group is provided with this book. Stochastic measures and scalar or operator bimeasures are fully discussed.
Author | : Christian Houdre |
Publisher | : |
Total Pages | : 29 |
Release | : 1988 |
Genre | : |
ISBN | : |
Some new classes of discrete time non-stationary processes, related to the harmonizable and V-bounded classes, are introduced. A few characterizations are obtained which, in turn, unify the V-bounded theory. Our main results depend on a special form of Grothendieck inequality. (JHD).
Author | : Randall J. Swift |
Publisher | : American Mathematical Society |
Total Pages | : 248 |
Release | : 2021-11-22 |
Genre | : Mathematics |
ISBN | : 1470459825 |
This volume contains the proceedings of the AMS Special Session on Celebrating M. M. Rao's Many Mathematical Contributions as he Turns 90 Years Old, held from November 9–10, 2019, at the University of California, Riverside, California. The articles show the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes and their applications. The volume also includes a biography of M. M. Rao and the list of his publications.
Author | : Malempati Madhusudana Rao |
Publisher | : World Scientific |
Total Pages | : 341 |
Release | : 2020-09-21 |
Genre | : Mathematics |
ISBN | : 9811213674 |
The book presents, for the first time, a detailed analysis of harmonizable processes and fields (in the weak sense) that contain the corresponding stationary theory as a subclass. It also gives the structural and some key applications in detail. These include Levy's Brownian motion, a probabilistic proof of the longstanding Riemann's hypothesis, random fields indexed by LCA and hypergroups, extensions to bistochastic operators, Cramér-Karhunen classes, as well as bistochastic operators with some statistical applications.The material is accessible to graduate students in probability and statistics as well as to engineers in theoretical applications. There are numerous extensions and applications pointed out in the book that will inspire readers to delve deeper.
Author | : Yuichiro Kakihara |
Publisher | : World Scientific |
Total Pages | : 343 |
Release | : 1997-02-27 |
Genre | : Mathematics |
ISBN | : 9814497894 |
This book provides a research-expository treatment of infinite-dimensional nonstationary stochastic processes or time series. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes and also the stationary class. Emphasis is on the use of functional, harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Readers may find that the covariance kernel analysis is emphasized and it reveals another aspect of stochastic processes. This book is intended not only for probabilists and statisticians, but also for communication engineers.
Author | : Jerome Goldstein |
Publisher | : CRC Press |
Total Pages | : 300 |
Release | : 2020-09-23 |
Genre | : Mathematics |
ISBN | : 1000148637 |
"Covers the areas of modern analysis and probability theory. Presents a collection of papers given at the Festschrift held in honor of the 65 birthday of M. M. Rao, whose prolific published research includes the well-received Marcel Dekker, Inc. books Theory of Orlicz Spaces and Conditional Measures and Applications. Features previously unpublished research articles by a host of internationally recognized scholars."
Author | : Harry L. Hurd |
Publisher | : John Wiley & Sons |
Total Pages | : 384 |
Release | : 2007-11-09 |
Genre | : Mathematics |
ISBN | : 9780470182826 |
Uniquely combining theory, application, and computing, this book explores the spectral approach to time series analysis The use of periodically correlated (or cyclostationary) processes has become increasingly popular in a range of research areas such as meteorology, climate, communications, economics, and machine diagnostics. Periodically Correlated Random Sequences presents the main ideas of these processes through the use of basic definitions along with motivating, insightful, and illustrative examples. Extensive coverage of key concepts is provided, including second-order theory, Hilbert spaces, Fourier theory, and the spectral theory of harmonizable sequences. The authors also provide a paradigm for nonparametric time series analysis including tests for the presence of PC structures. Features of the book include: An emphasis on the link between the spectral theory of unitary operators and the correlation structure of PC sequences A discussion of the issues relating to nonparametric time series analysis for PC sequences, including estimation of the mean, correlation, and spectrum A balanced blend of historical background with modern application-specific references to periodically correlated processes An accompanying Web site that features additional exercises as well as data sets and programs written in MATLAB® for performing time series analysis on data that may have a PC structure Periodically Correlated Random Sequences is an ideal text on time series analysis for graduate-level statistics and engineering students who have previous experience in second-order stochastic processes (Hilbert space), vector spaces, random processes, and probability. This book also serves as a valuable reference for research statisticians and practitioners in areas of probability and statistics such as time series analysis, stochastic processes, and prediction theory.
Author | : R.M. Dudley |
Publisher | : Springer Science & Business Media |
Total Pages | : 512 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461203678 |
Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly.