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Selected Works of R.M. Dudley

Sofort lieferbar | Lieferzeit: Sofort lieferbar I
ISBN-13:
9781441958211
Veröffentl:
2010
Seiten:
481
Autor:
Evarist Giné
Serie:
Selected Works in Probability and Statistics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:

For almost fifty years, Richard M. Dudley has been extremely influential in the development of several areas of Probability. His work on Gaussian processes led to the understanding of the basic fact that their sample boundedness and continuity should be characterized in terms of proper measures of complexity of their parameter spaces equipped with the intrinsic covariance metric. His sufficient condition for sample continuity in terms of metric entropy is widely used and was proved by X. Fernique to be necessary for stationary Gaussian processes, whereas its more subtle versions (majorizing measures) were proved by M. Talagrand to be necessary in general.
Convergence in Law.- Weak Convergence of Probabilities on Nonseparable Metric Spaces and Empirical Measures on Euclidean Spaces.- Measures on Non-Separable Metric Spaces.- Distances of Probability Measures and Random Variables.- An Extended Wichura Theorem, Definitions of Donsker Class, and Weighted Empirical Distributions.- Markov Processes.- Lorentz-invariant Markov processes in relativistic phase space.- A note on Lorentz-invariant Markov processes.- Asymptotics of Some Relativistic Markov Processes.- Gaussian Processes.- The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes.- On seminorms and probabilities, and abstract Wiener spaces.- Sample Functions of the Gaussian Process.- On the Lower Tail of Gaussian Seminorms.- Empirical Processes.- Special Invited Paper.- Empirical and Poisson Processes on Classes of Sets or Functions Too Large for Central Limit Theorems.- Invariance Principles for Sums of Banach Space Valued Random Elements and Empirical Processes.- Universal Donsker Classes and Metric Entropy.- Nonlinear functionals and p-variation.- Fréchet Differentiability, p-Variation and Uniform Donsker Classes.- The Order of the Remainder in Derivatives of Composition and Inverse Operators for p-Variation Norms.- Empirical Processes and p-variation.- Miscellanea.- Pathological Topologies and Random Walks on Abelian Groups.- Metric Entropy of Some Classes of Sets with Differentiable Boundaries.- Wiener Functionals as Itô Integrals.- A Metric Entropy Bound is Not Sufficient for Learnability.- Asymptotic Normality with Small Relative Errors of Posterior Probabilities of Half-Spaces.

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