**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 Processes

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*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.

#### Readership

Graduate students and research mathematicians interested in probability theory and stochastic processes.

#### Reviews & Endorsements

The analytical and formal-theoretical perspective of this book could be used as a basis for future historical and quantitative studies.

-- Zentralblatt MATH