Translations of Mathematical Monographs 2000; 257 pp; hardcover Volume: 188 ISBN10: 0821805339 ISBN13: 9780821805336 List Price: US$103 Member Price: US$82.40 Order Code: MMONO/188
 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: preGaussian processes, shot noise processes representable as integrals over processes with independent increments, quadratically Gaussian processes, and, in particular, correlogramtype estimates of the correlation function of a stationary Gaussian process, jointly strictly subGaussian 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 "The analytical and formaltheoretical perspective of this book could be used as a basis for future historical and quantitative studies."  Zentralblatt MATH Table of Contents  SubGaussian and preGaussian random variables
 Orlicz spaces of random variables
 Regularity of sample paths of a stochastic process
 PreGaussian processes
 Shot noise processes and their properties
 Correlograms of stationary Gaussian processes
 Jointly subGaussian, superGaussian, and pseudoGaussian stochastic processes
 Appendices
 Comments
 References
 Basic notation
 Index
