Introduction.- Stochastic Evolution Equations in Hilbert Spaces.- Optimal Strong Error Estimates for Galerkin Finite Element Methods.- A Short Review of the Malliavin Calculus in Hilbert Spaces.- A Malliavin Calculus Approach to Weak Convergence.- Numerical Experiments.- Some Useful Variations of Gronwall's Lemma.- Results on Semigroups and their Infinitesimal Generators.- A Generalized Version of Lebesgue's Theorem.- References.- Index.
Описание: This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.
Описание: The purpose of this book is to present results on the subject of weak convergence in function spaces to study invariance principles in statistical applications to dependent random variables, U-statistics, censor data analysis. Different techniques, formerly available only in a broad range of literature, are for the first time presented here in a self-contained fashion. Contents:Weak convergence of stochastic processesWeak convergence in metric spacesWeak convergence on C[0, 1] and D[0,?)Central limit theorem for semi-martingales and applicationsCentral limit theorems for dependent random variablesEmpirical processBibliography
Автор: Vaart, Aad Van Der Wellner, Jon A. Название: Weak convergence and empirical processes ISBN: 1475725477 ISBN-13(EAN): 9781475725476 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book explores weak convergence theory and empirical processes and their applications to many applications in statistics. Part two offers the theory of empirical processes in a form accessible to statisticians and probabilists.
Название: Methods of fourier analysis and approximation theory ISBN: 3319274651 ISBN-13(EAN): 9783319274652 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Different facets of interplay between harmonic analysis andapproximation theory are covered in this volume. The topics included areFourier analysis, function spaces, optimization theory, partial differentialequations, and their links to modern developments in the approximation theory.
Автор: J?rome Dedecker; Paul Doukhan; Gabriel Lang; Jos? Название: Weak Dependence: With Examples and Applications ISBN: 0387699511 ISBN-13(EAN): 9780387699516 Издательство: Springer Рейтинг: Цена: 18167.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Develops Doukhan/Louhichi`s 1999 idea to measure asymptotic independence of a random process.
Автор: FITZMAURICE; GURARIE; MCCAUGHAN; WOYCZYNSKI Название: Nonlinear Waves and Weak Turbulence ISBN: 1461267110 ISBN-13(EAN): 9781461267119 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is an outgrowth of the NSF-CBMS conference Nonlinear Waves GBP3 Weak Turbulence held at Case Western Reserve University in May 1992. Work in field can be broadly divided into two areas: * The theory of the transition from smooth laminar motions to the disordered motions characteristic of turbulence.
Описание: It may also serve as an excellent self-study reference for electrical engineers and applied mathematicians whose work is related to the fields of electronics, signal processing, image and speech processing, or digital design and communication.
Автор: Iske, Armin Название: Approximation theory and algorithms for data analysis ISBN: 3030052273 ISBN-13(EAN): 9783030052270 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role.The following topics are covered:* least-squares approximation and regularization methods* interpolation by algebraic and trigonometric polynomials* basic results on best approximations* Euclidean approximation* Chebyshev approximation* asymptotic concepts: error estimates and convergence rates* signal approximation by Fourier and wavelet methods* kernel-based multivariate approximation* approximation methods in computerized tomographyProviding numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.
Автор: Francesco Altomare, Mirella Cappelletti, Vita Leon Название: Markov Operators, Positive Semigroups and Approximation Processes ISBN: 3110372746 ISBN-13(EAN): 9783110372748 Издательство: Walter de Gruyter Цена: 26024.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This research monograph gives a detailed account of a theory which is mainly concerned with certain classes of degenerate differential operators, Markov semigroups and approximation processes. These mathematical objects are generated by arbitrary Markov operators acting on spaces of continuous functions defined on compact convex sets; the study of the interrelations between them constitutes one of the distinguishing features of the book. Among other things, this theory provides useful tools for studying large classes of initial-boundary value evolution problems, the main aim being to obtain a constructive approximation to the associated positive C0-semigroups by means of iterates of suitable positive approximating operators. As a consequence, a qualitative analysis of the solutions to the evolution problems can be efficiently developed. The book is mainly addressed to research mathematicians interested in modern approximation theory by positive linear operators and/or in the theory of positive C0-semigroups of operators and evolution equations. It could also serve as a textbook for a graduate level course.
Описание: This book, meant for graduate students and researchers, explores the connections between numerical approximation and statistical inference from a game and decision theoretic perspective, and illustrates these interplays by addressing problems related to numerical homogenization, operator adapted wavelets, and fast solvers.
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