Gaussian Random FunctionsSpringer Science & Business Media, 28 févr. 1995 - 337 pages 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 |
Table des matières
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 |
| 295 | |
| 327 | |
LIST OF BASIC NOTATIONS | 331 |
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Expressions et termes fréquents
admissible shifts arbitrary Assume ball Banach space barycenter Borel bound boundedness Brownian bridge Brownian function Brownian motion centered Gaussian compact condition constructed continuous covariance function covariance operator defined definition density English translation entropy equality estimate Fernique finite formula function f Gaussian distribution Gaussian field Gaussian measure Gaussian processes Gaussian random function Hilbert space holds inequality integral ISBN isoperimetric iterated logarithm kernel large deviations Lemma Lévy's lim sup linear functionals majorizing measure Math metric entropy norm obtain oscillation parameter Primenen probabilities of large Proof Proposition proved Radon measure random variables random vector Russian sample functions Section seminorm sequence small deviations standard Gaussian stationary stationary process Stochastic Strassen Strassen's law subspace symmetric Teor Theorem Theory Probab tion translation in Theory Veroyatn weak topology Wiener process zero