Articoli correlati a Gaussian Random Functions: 322
Sinossi
This text presents a mathematically complete series of the most essential properties of Gaussian random functions. It focuses on a number of fundamental objects in the theory of Gaussian random functions and exposes their interrelations. The basic plots presented in the book embody: the kernel of a Gaussian measure; the model of a Gaussian random function; oscillations of sample functions; the convexity and isoperimetric inequalities; the regularity of sample functions of means of entropy characteristics and the majorizing measures; functional laws of the iterated logarithm and estimates for the probabilities of large deviations. This book should be of interest to mathematicians and scientists who use stochastic methods in their research and to students in probability theory.
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Contenuti
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.
Product Description
Book by Lifshits MA
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Gaussian Random Functions (Mathematics and Its Applications, 322)
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Gaussian Random Functions
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Gebunden. Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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. Codice articolo 458438657
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Gaussian Random Functions (Mathematics and Its Applications, 322)
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