by Yûichirô Kakihara (University of California, Riverside)

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.

• Introduction and Preliminaries
• Hilbert Modules and Covariance Kernels
• Stochastic Measures and Operator-Valued Bimeasures
• Multidimensional Stochastic Processes
• Special Topics
• Applications