Stationary Stochastic Processes Theory And Applications

"Preface This book has grown out of my own experiences as teacher and researcher at a department in mathematical statistics with responsibilities both to an engineering and a science community. The spirit of the text reflects those double responsibilities. The background The book Stationary and Related Stochastic Processes [34] appeared in 1967. Written by Harald Cramér and M.R. Leadbetter, it drastically changed the life of PhD students in Mathematical statistics with an interest in stochastic processes and their applications, as well as that of students in many other fields of science and engineering. Through that book, they got access to tools and results for stationary stochastic processes that until then had been available only in rather advanced mathematical textbooks, or through specialized statistical journals. The impact of the book can be judged from the fact that still, after almost fifty years, it is a standard reference to stationary processes in PhD theses and research articles. Even if many of the more specialized results in the Cramér-Leadbetter book have been superseded by more general results, and simpler proofs have been found for some of the statements, the general attitude in the book makes it enjoyable reading both for the student and for the teacher. It will remain a definite source of reference for many standard results on sample function and crossings properties of continuous time processes, in particular in the Gaussian case"--