Gaussian Random Functions

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 me...

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Bibliographic Details
Main Author: Lifshits, M.A.
Format: eBook
Language:English
Published: Dordrecht Springer Netherlands 1995, 1995
Edition:1st ed. 1995
Series:Mathematics and Its Applications
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Section 1. Gaussian distributions and random variables
  • Section 2. Multi-dimensional Gaussian distributions
  • Section 3. Covariances
  • Section 4. Random functions
  • Section 5. Examples of Gaussian random functions
  • Section 6. Modelling the covariances
  • Section 7. Oscillations
  • Section 8. Infinite-dimensional Gaussian distributions
  • Section 9. Linear functionals, admissible shifts, and the kernel
  • Section 10. The most important Gaussian distributions
  • Section 11. Convexity and the isoperimetric inequality
  • Section 12. The large deviations principle
  • Section 13. Exact asymptotics of large deviations
  • Section 14. Metric entropy and the comparison principle
  • Section 15. Continuity and boundedness
  • Section 16. Majorizing measures
  • Section 17. The functional law of the iterated logarithm
  • Section 18. Small deviations
  • Section 19. Several open problems
  • Comments
  • References
  • List of Basic Notations