Gaussian Random Functions

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Springer Science & Business Media, Feb 28, 1995 - Mathematics - 337 pages
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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
 

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Contents

GAUSSIAN DISTRIBUTIONS AND RANDOM VARIABLES
1
MULTIDIMENSIONAL GAUSSIAN DISTRIBUTIONS
8
COVARIANCES
16
RANDOM FUNCTIONS
22
EXAMPLES OP GAUSSIAN RANDOM FUNCTIONS
30
MODELLING THE COVARIANCES
41
OSCILLATIONS
53
INFINITEDIMENSIONAL GAUSSIAN DISTRIBUTIONS
68
EXACT ASYMPTOTICS OF LARGE DEVIATIONS
156
METRIC ENTROPY AND THE COMPARISON PRINCIPLE
177
CONTINUITY AND BOUNDEDNESS
211
MAJORIZING MEASURES
230
THE FUNCTIONAL LAW OF THE ITERATED LOGARITHM
246
SMALL DEVIATIONS
258
SEVERAL OPEN PROBLEMS
276
COMMENTS
282

LINEAR FUNCTIONALS ADMISSIBLE SHIFTS AND THE KERNEL
84
THE MOST IMPORTANT GAUSSIAN DISTRIBUTIONS
101
CONVEXITY AND THE ISOPERIMETRIC PROPERTY
108
THE LARGE DEVIATIONS PRINCIPLE
139
REFERENCES
295
SUBJECT INDEX
327
LIST OF BASIC NOTATIONS
331
Copyright

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Page 308 - The law of the iterated logarithm for Brownian motion in a Banach space Trans.
Page 316 - On Strassen's version of the law of the iterated logarithm for Gaussian processes.
Page 310 - La transformation de Laplace dans les espaces lineaires. CR Acad. Sci. Paris 200, 1717—1718.
Page 321 - SEGAL, IE, Abstract Probability Spaces and a Theorem of Kolmogoroff, Amer. J. Math., Vol.

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