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140122  eng 
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a 9789401584746

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1 

a Lifshits, M.A.

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a Gaussian Random Functions
h Elektronische Ressource
c by M.A. Lifshits

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a 1st ed. 1995

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a Dordrecht
b Springer Netherlands
c 1995, 1995

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a XI, 337 p. 2 illus
b online resource

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0 

a Section 1. Gaussian distributions and random variables  Section 2. Multidimensional 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. Infinitedimensional 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

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a Functional analysis

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a Measure theory

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a Functional Analysis

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a Statistics

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a Probability Theory

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a Measure and Integration

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a Statistics

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a Probabilities

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0 
7 
a eng
2 ISO 6392

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b SBA
a Springer Book Archives 2004

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a Mathematics and Its Applications

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a 10.1007/9789401584746

856 
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u https://doi.org/10.1007/9789401584746?nosfx=y
x Verlag
3 Volltext

082 
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a 519.2

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a 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 infinitedimensional 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 "onedimensional" properties are extended almost literally, while some others should be profoundly justified, or even must be reconsidered. What is more, the infinitedimensional 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 sixtiesseventies, 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
