Translations of Mathematical Monographs
2000; 257 pp; Hardcover
MSC: Primary 60;
Print ISBN: 978-0-8218-0533-6
Product Code: MMONO/188
List Price: $109.00
Individual Member Price: $87.20
Metric Characterization of Random Variables and Random ProcessesShare this page
V. V. Buldygin; Yu. V. Kozachenko
The topic covered in this book is the study of metric and other
close characteristics of different spaces and classes of random
variables and the application of the entropy method to the
investigation of properties of stochastic processes whose values, or
increments, belong to given spaces. The following processes appear in
detail: pre-Gaussian processes, shot noise processes representable as
integrals over processes with independent increments, quadratically
Gaussian processes, and, in particular, correlogram-type estimates of
the correlation function of a stationary Gaussian process, jointly
strictly sub-Gaussian processes, etc.
The book consists of eight chapters divided into four parts: The first part deals with classes of random variables and their metric characteristics. The second part presents properties of stochastic processes “imbedded” into a space of random variables discussed in the first part. The third part considers applications of the general theory. The fourth part outlines the necessary auxiliary material.
Problems and solutions presented show the intrinsic relation existing between probability methods, analytic methods, and functional methods in the theory of stochastic processes. The concluding sections, “Comments” and “References”, gives references to the literature used by the authors in writing the book.
Table of Contents
Table of Contents
Metric Characterization of Random Variables and Random Processes
Graduate students and research mathematicians interested in probability theory and stochastic processes.
The analytical and formal-theoretical perspective of this book could be used as a basis for future historical and quantitative studies.
-- Zentralblatt MATH