Stationary and Related Stochastic Processes

About this book

This book is written for a reader assumed to have a working knowledge of the basic features of modern probability theory. Some fundamental concepts and propositions of this this theory are briefly reviewed (Chapter 2). The foundations of the general theory of stochastic processes are then developed with special emphasis on processes with a continuous-time parameter (Chapter3). The analytic properties of the trajectories such as continuity differentiability etc. are studied in some detail (Chapter 4). The general theory is then applied to certain classes of processes important as tools for the study of stationary processes (Chapters 5 and 6). Then main part of the book is concerned with the theory and applications of stationary processes i.e. Hilbert space geometry ergodic theorems etc. (Chapter 7). Certain generalizations are treated in a separate chapter (Chapter 8). Normal (Gaussian) stationary processes are thoroughly studied (Chapter 9). The problem of the time distribution of the intersection between a sample function and a given constant level with problems discussed and several results that are believed to be new are presented (Chapters 10 to 13). Various application to problems of frequency and reliability are given (Chapters 14 and 15).