"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 o…
Introduction and preliminaries -- Hilbert modules and covariance kernels -- Stochastic measures and operator valued bimeasures -- Radon-Nikodým derivatives and Schauder basic measures -- Multidimensional stochastic processes -- Special topics -- Applications -- Generalizations. …
"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"--
"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"--
Ch. I. Entropy. 1.1. The Shannon entropy. 1.2. Conditional expectations. 1.3. The Kolmogorov-. Sinai entropy. 1.4. Algebraic models. 1.5. Entropy functionals. 1.6. Relative entropy and Kullback-Leibler information -- ch. II. Information sources. 2.1. Alphabet message spaces and …
Information Theory is studied from the following view points: (1) the theory of entropy as amount of information; (2) the mathematical structure of information sources (probability measures); and (3) the theory of information channels. Shannon entropy and Kolmogorov-Sinai entrop…
This book provides a research-expository treatment of infinite-dimensional nonstationary stochastic processes or times series. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary proces…
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 process…