Gaussian Random Functions

ISBN-13: 9780792333852 / Angielski / Twarda / 1995 / 337 str.

M. A. Lifshits

Opis

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

Spis treści

Preface. 1: Gaussian distributions and random variables. 2: Multi-dimensional Gaussian distributions. 3: Covariances. 4: Random functions. 5: Examples of Gaussian random functions. 6: Modelling the covariances. 7: Oscillations. 8: Infinite-dimensional Gaussian distributions. 9: Linear functionals, admissible shifts, and the kernel. 10: The most important Gaussian distributions. 11: Convexity and the isoperimetric inequality. 12: The large deviations principle. 13: Exact asymptotics of large deviations. 14: Metric entropy and the comparison principle. 15: Continuity and boundedness. 16: Majorizing measures. 17: The functional law of the iterated logarithm. 18: Small deviations. 19: Several open problems. Comments. References. Subject index. List of basic notations.