Uniform Central Limit Theorems(2nd Edition) (Cambridge Studies in Advanced Mathematics) by R. M. Dudley Hardcover, 486 Pages, Published 2014 by Cambridge University Press ISBN-13: 978-0-521-49884-5, ISBN: 0-521-49884-8
"This classic work on empirical processes has been considerably expanded and revised from the original edition. When samples become large, the probability laws of large numbers and central limit theorems are guaranteed to hold uniformly over wide domains. The author, an acknowledged expert, gives a thorough treatment of the subject, including the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment ..."
"Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients. In this book existence and uniqueness of solutions are ..."
"The optical fiber based supercontinuum source has recently become a significant scientific and commercial success, with applications ranging from frequency comb production to advanced medical imaging. This one-of-a-kind book explains the theory of fiber supercontinuum broadening, describes the diverse operational regimes and indicates principal areas of applications, making it a very important guide for researchers and graduate students ..."
"Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in suc ..."
"J. O. Stevenson. Holomorphy of composition. Bull. Amer. Math. Soc. 80 (1974),
300–303. J. O. Stevenson. Holomorphy of composition. In: Infinite Dimensional
Holomorphy and Applications (M. C. Matos, ed.), 397–424. North-Holland,
Amsterdam, 1977. ∗T. J. Stieltjes. Recherches sur les fractions continues. Ann.
Fac. Sci. Toulouse Sér. 18 (1894), 1–122; 9 (1895), 1–47. B. Szénássy. History of
Mathematics in Hungary until the 20th Century ..."
Uniform Central Limit Theorems(Reprint) (Cambridge Studies in Advanced Mathematics) by R. M. Dudley Paperback, 452 Pages, Published 2008 by Cambridge University Press ISBN-13: 978-0-521-05221-4, ISBN: 0-521-05221-1
"This book shows how the central limit theorem for independent, identically distributed random variables with values in general, multidimensional spaces, holds uniformly over some large classes of functions. The author, an acknowledged expert, gives a thorough treatment of the subject, including several topics not found in any previous book, such as the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended tre ..."
"Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients. In this book existence and uniqueness of solutions are ..."
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"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 ..."
"xvi A Biographical Sketch of Richard M. Dudley p-variation and in differentiable
functionals, in connection with the delta method for statistical functionals. ... J.
Kuelbs, S. R. Kulkarni, J. Llopis, L. Pakula, N. P. Peng, P. Perkins, W. Philipp, A.
Quiroz, B. Randol, T. J. Richardson, L. Shepp, S. Sidenko, D. Smith, D. Stroock, F.
Topsøe, Z. Wang, R. S. Wenocur, O. Zeitouni, J. Zinn, and the editors of this
volume."
Uniform Central Limit Theorems(2nd Edition) (Cambridge Studies in Advanced Mathematics) by Richard M. Dudley Paperback, 482 Pages, Published 2014 by Cambridge University Press ISBN-13: 978-0-521-73841-5, ISBN: 0-521-73841-5
"This classic work on empirical processes has been considerably expanded and revised from the original edition. When samples become large, the probability laws of large numbers and central limit theorems are guaranteed to hold uniformly over wide domains. The author, an acknowledged expert, gives a thorough treatment of the subject, including the Fernique-Talagrand majorizing measure theorem for Gaussian processes, an extended treatment ..."
"This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level.Texts that are out of print but still in demand may also be considered.The timeliness of a manuscript is sometimes more important than its form, which may in such cases be preliminary or tentative.Details of the editorial policy and how to submit can be found at www.springer.com/series/304. We recommend contacting the ..."
"This classic textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The first half of the book gives an exposition of real analysis: basic set theory, general topology, measure theory, integration, an introduction to functional analysis in Banach and Hilbert spaces, convex sets and functions and measure on topological spaces. The second half ..."