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Metric Characterization of Random Variables and Random Processes
 
V. V. Buldygin Kyïv Politechnic Institute, Kyïv, Ukraine
Yu. V. Kozachenko Kyïv Taras Shevchenko National University, Kyïv, Ukraine
Metric Characterization of Random Variables and Random Processes
Hardcover ISBN:  978-0-8218-0533-6
Product Code:  MMONO/188
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4602-4
Product Code:  MMONO/188.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-0533-6
eBook: ISBN:  978-1-4704-4602-4
Product Code:  MMONO/188.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Metric Characterization of Random Variables and Random Processes
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Metric Characterization of Random Variables and Random Processes
V. V. Buldygin Kyïv Politechnic Institute, Kyïv, Ukraine
Yu. V. Kozachenko Kyïv Taras Shevchenko National University, Kyïv, Ukraine
Hardcover ISBN:  978-0-8218-0533-6
Product Code:  MMONO/188
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4602-4
Product Code:  MMONO/188.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-0533-6
eBook ISBN:  978-1-4704-4602-4
Product Code:  MMONO/188.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 1882000; 257 pp
    MSC: Primary 60

    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.

  • Table of Contents
     
     
    • Chapters
    • Sub-Gaussian and pre-Gaussian random variables
    • Orlicz spaces of random variables
    • Regularity of sample paths of a stochastic process
    • Pre-Gaussian processes
    • Shot noise processes and their properties
    • Correlograms of stationary Gaussian processes
    • Jointly sub-Gaussian, super-Gaussian, and pseudo-Gaussian stochastic processes
    • Appendices
  • Additional Material
     
     
  • Reviews
     
     
    • The analytical and formal-theoretical perspective of this book could be used as a basis for future historical and quantitative studies.

      Zentralblatt MATH
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1882000; 257 pp
MSC: Primary 60

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.

  • Chapters
  • Sub-Gaussian and pre-Gaussian random variables
  • Orlicz spaces of random variables
  • Regularity of sample paths of a stochastic process
  • Pre-Gaussian processes
  • Shot noise processes and their properties
  • Correlograms of stationary Gaussian processes
  • Jointly sub-Gaussian, super-Gaussian, and pseudo-Gaussian stochastic processes
  • Appendices
  • The analytical and formal-theoretical perspective of this book could be used as a basis for future historical and quantitative studies.

    Zentralblatt MATH
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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