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Gaussian Random Functions

  • M. A. Lifshits

Part of the Mathematics and Its Applications book series (MAIA, volume 322)

Table of contents

  1. Front Matter
    Pages i-xi
  2. M. A. Lifshits
    Pages 8-15
  3. M. A. Lifshits
    Pages 16-21
  4. M. A. Lifshits
    Pages 22-29
  5. M. A. Lifshits
    Pages 30-40
  6. M. A. Lifshits
    Pages 41-52
  7. M. A. Lifshits
    Pages 53-67
  8. M. A. Lifshits
    Pages 68-83
  9. M. A. Lifshits
    Pages 101-107
  10. M. A. Lifshits
    Pages 108-138
  11. M. A. Lifshits
    Pages 139-155
  12. M. A. Lifshits
    Pages 156-176
  13. M. A. Lifshits
    Pages 177-210
  14. M. A. Lifshits
    Pages 211-229
  15. M. A. Lifshits
    Pages 230-245
  16. M. A. Lifshits
    Pages 246-257
  17. M. A. Lifshits
    Pages 258-275
  18. M. A. Lifshits
    Pages 276-281
  19. Back Matter
    Pages 282-337

About this book

Introduction

It is well known that the normal distribution is the most pleasant, one can even say, an exemplary object in the probability theory. It combines almost all conceivable nice properties that a distribution may ever have: symmetry, stability, indecomposability, a regular tail behavior, etc. Gaussian measures (the distributions of Gaussian random functions), as infinite-dimensional analogues of tht< classical normal distribution, go to work as such exemplary objects in the theory of Gaussian random functions. When one switches to the infinite dimension, some "one-dimensional" properties are extended almost literally, while some others should be profoundly justified, or even must be reconsidered. What is more, the infinite-dimensional situation reveals important links and structures, which either have looked trivial or have not played an independent role in the classical case. The complex of concepts and problems emerging here has become a subject of the theory of Gaussian random functions and their distributions, one of the most advanced fields of the probability science. Although the basic elements in this field were formed in the sixties-seventies, it has been still until recently when a substantial part of the corresponding material has either existed in the form of odd articles in various journals, or has served only as a background for considering some special issues in monographs.

Keywords

Gaussian distribution Gaussian measure Probability theory Variance distribution law of the iterated logarithm random function

Authors and affiliations

  • M. A. Lifshits
    • 1
  1. 1.St. Petersburg University of Finance and EconomicsSt. PetersburgRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8474-6
  • Copyright Information Springer Science+Business Media B.V. 1995
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4528-7
  • Online ISBN 978-94-015-8474-6
  • Buy this book on publisher's site
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