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Gaussian Random Functions : Mathematics and Its Applications - M. A. Lifshits

Gaussian Random Functions

Mathematics and Its Applications

Hardcover Published: 28th February 1995
ISBN: 9780792333852
Number Of Pages: 337

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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.

Gaussian distributions and random variablesp. 1
Multi-dimensional Gaussian distributionsp. 8
Covariancesp. 16
Random functionsp. 22
Examples of Gaussian random functionsp. 30
Modelling the covariancesp. 41
Oscillationsp. 53
Infinite-dimensional Gaussian distributionsp. 68
Linear functionals, admissible shifts, and the kernelp. 84
The most important Gaussian distributionsp. 101
Convexity and the isoperimetric inequalityp. 108
The large deviations principlep. 139
Exact asymptotics of large deviationsp. 156
Metric entropy and the comparison principlep. 177
Continuity and boundednessp. 211
Majorizing measuresp. 230
The functional law of the iterated logarithmp. 246
Small deviationsp. 258
Several open problemsp. 276
Commentsp. 282
Referencesp. 295
Subject Indexp. 327
List of Basic Notationsp. 331
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792333852
ISBN-10: 0792333853
Series: Mathematics and Its Applications
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 337
Published: 28th February 1995
Country of Publication: NL
Dimensions (cm): 24.23 x 16.41  x 2.46
Weight (kg): 0.67

Earn 678 Qantas Points
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