Selected Works of R.M. Dudley

• Corporate Author: SpringerLink (Online service)
• Other Authors: Gin,̌ Evarist. (Editor), Koltchinskii, Vladimir. (Editor), Norvaisa, Rimas. (Editor)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2010.
• Series: Selected Works in Probability and Statistics
• Subjects: Mathematics.; Distribution (Probability theory).; Mathematical statistics.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4419-5821-1

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 c...

Table of Contents:

• Chapter 1: 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
• Chapter 2: Markov Processes: Lorentz-invariant Markov processes in relativistic phase space
• A note on Lorentz-invariant Markov processes
• Asymptotics of some relativistic Markov processes
• Chapter 3: 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
• Chapter 4: Empirical Processes: Central limit theorems for empirical measures
• 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 variables and empirical processes
• Universal Donsker classes and metric entropy
• Chapter 5: Nonlinear functionals and p-variation: Frčhet 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
• Chapter 6: Miscellanea: Pathological topologies and random walks on Abelian groups
• Metric entropy of some classes of sets with differentiable boundaries
• In Wiener functionals as It ̥integrals
• A metric entropy bound is not sufficient for learnability
• Asymptotic normality with small relative errors of posterior probabilities of half-spaces.