Hilbert And Banach Space-valued Stochastic Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hilbert And Banach Space-valued Stochastic Processes write by Yuichiro Kakihara. This book was released on 2021-07-29. Hilbert And Banach Space-valued Stochastic Processes available in PDF, EPUB and Kindle. 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.
Multidimensional Second Order Stochastic Processes
Multidimensional Second Order Stochastic Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multidimensional Second Order Stochastic Processes write by Yuichiro Kakihara. This book was released on 1997-02-27. Multidimensional Second Order Stochastic Processes available in PDF, EPUB and Kindle. 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.
Hilbert and Banach Space-valued Stochastic Processes
Hilbert and Banach Space-valued Stochastic Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hilbert and Banach Space-valued Stochastic Processes write by Yūichirō Kakihara. This book was released on 2021. Hilbert and Banach Space-valued Stochastic Processes available in PDF, EPUB and Kindle. "Functional analysis methods are used on stochastic processes. Structural analysis of nonstationary and stationary processes are also included. This book is in the intersection of probability theory and analysis"--
Banach Space Valued Stationary Stochastic Processes and Factorization of Nonnegative Operator Valued Functions on a Banach Space
Banach Space Valued Stationary Stochastic Processes and Factorization of Nonnegative Operator Valued Functions on a Banach Space - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Banach Space Valued Stationary Stochastic Processes and Factorization of Nonnegative Operator Valued Functions on a Banach Space write by Abolghassem G. Miamee. This book was released on 1973. Banach Space Valued Stationary Stochastic Processes and Factorization of Nonnegative Operator Valued Functions on a Banach Space available in PDF, EPUB and Kindle.
Probability in Banach Spaces
Probability in Banach Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Probability in Banach Spaces write by Michel Ledoux. This book was released on 2013-03-09. Probability in Banach Spaces available in PDF, EPUB and Kindle. Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.
