Hilbert And Banach Space-valued Stochastic Processes

This book discusses infinite-dimensional stationary and nonstationary stochastic processes or time series,based on Hilbert and Banach space-valued second order random variables. It develops integral representations of various classes of nonstationary processes and introduces a new type of Radon-Nikodým derivative of a Banach space-valued measure. Applications are made to prediction problems, Kalman filter, sampling theorems, and strong laws of large numbers. Generalizations are made to consider processes of pth order for p ≥ 1.

\n Format: Hardback
\n Length: 540 pages
\n Publication date: 12 May 2021
\n Publisher: World Scientific Publishing Co Pte Ltd
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This book is a comprehensive and in-depth exploration of infinite-dimensional stationary and nonstationary stochastic processes, also known as time series. It builds upon the foundation of the earlier book, Multidimensional Second Order Stochastic Processes, and delves deeper into the realm of Hilbert and Banach space-valued second order random variables. The author provides a research expository treatment that covers a wide range of topics, including stochastic measures, scalar or operator bimeasures, and integral representations of various classes of nonstationary processes.

The book begins by introducing stochastic measures and scalar or operator bimeasures, which play a crucial role in developing integral representations of nonstationary processes. It discusses the development of integral representations for harmonizable, V-bounded, Cramér, and Karhunen classes, as well as the stationary class. A novel type of Radon-Nikodým derivative of a Banach space-valued measure is introduced, along with Schauder basic measures, to study uniformly bounded linearly stationary processes.

The emphasis throughout the book is on the use of functional analysis, harmonic analysis, and probability theory to study stochastic processes. The author applies these tools to various applications, such as prediction problems, Kalman filters, sampling theorems, and strong laws of large numbers. Generalizations are made to consider Banach space-valued stochastic processes for higher-order processes, where p ≥ 1.

One notable aspect of the book is the constant emphasis on the covariance kernel, which reveals another dimension of stochastic processes. The author highlights the importance of understanding the covariance kernel in analyzing and understanding stochastic systems.

This book is designed to appeal to a wide audience, including probabilists, statisticians, functional analysts, and communication engineers. It provides a solid foundation in stochastic processes and offers valuable insights into their applications in various fields. The clear and concise writing style makes it accessible to students and professionals alike.

In conclusion, this book is a valuable resource for anyone interested in the study of infinite-dimensional stationary and nonstationary stochastic processes. It offers a comprehensive treatment of the subject, combining theoretical analysis with practical applications, and is written in a manner that is accessible to a broad audience. Whether you are a researcher, practitioner, or simply seeking to expand your knowledge in this area, this book is an excellent choice.

\n Weight: 918g\n
Dimension: 160 x 237 x 36 (mm)\n
ISBN-13: 9789811211744\n \n