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Weak Convergence Ia
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Book Synopsis Weak Convergence (IA) by : Tchilabalo Abozou Kpanzou
Download or read book Weak Convergence (IA) written by Tchilabalo Abozou Kpanzou and published by Independently Published. This book was released on 2021-11-08 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aims at presenting the core weak convergence theory for sequences of random vectors with values in dimension k. In some places, a more general formulation in metric spaces is provided. It lays out the necessary foundation that paves the way to applications in particular sub-fields of the theory. In particular, the needs of Asymptotic Statistics are addressed. A whole chapter is devoted to weak convergence in the real line where specific tools, for example for handling weak convergence of sequences using independent and identically distributed random variables such that the Renyi's representations by means of standard uniform or exponential random variables, are stated. The functional empirical process is presented as a powerful tool for solving a considerable number of asymptotic problems in Statistics. The text is written in a self-contained approach with the proofs of all used results at the exception of the general Skorohod-Wichura Theorem. We finish the book with a chapter on weak convergence of bounded measures and locally bounded measures in preparation of a more general theory of measures on topological spaces
Book Synopsis Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems by : Harold Kushner
Download or read book Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).
Book Synopsis Weak Convergence of Measures by : Vladimir I. Bogachev
Download or read book Weak Convergence of Measures written by Vladimir I. Bogachev and published by American Mathematical Society. This book was released on 2024-07-29 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough exposition of the main concepts and results related to various types of convergence of measures arising in measure theory, probability theory, functional analysis, partial differential equations, mathematical physics, and other theoretical and applied fields. Particular attention is given to weak convergence of measures. The principal material is oriented toward a broad circle of readers dealing with convergence in distribution of random variables and weak convergence of measures. The book contains the necessary background from measure theory and functional analysis. Large complementary sections aimed at researchers present the most important recent achievements. More than 100 exercises (ranging from easy introductory exercises to rather difficult problems for experienced readers) are given with hints, solutions, or references. Historic and bibliographic comments are included. The target readership includes mathematicians and physicists whose research is related to probability theory, mathematical statistics, functional analysis, and mathematical physics.
Book Synopsis Weak Convergence and Empirical Processes by : Aad van der vaart
Download or read book Weak Convergence and Empirical Processes written by Aad van der vaart and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores weak convergence theory and empirical processes and their applications to many applications in statistics. Part one reviews stochastic convergence in its various forms. Part two offers the theory of empirical processes in a form accessible to statisticians and probabilists. Part three covers a range of topics demonstrating the applicability of the theory to key questions such as measures of goodness of fit and the bootstrap.
Book Synopsis Weak Convergence and the Prediction Process by : Hideatsu Tsukahara
Download or read book Weak Convergence and the Prediction Process written by Hideatsu Tsukahara and published by . This book was released on 1996 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: We first consider convergence in law of measurable processes with a general parameter set and a state space. To this end, we need to investigate topological properties of the space of measurable functions which is the paths space of measurable processes. Also a characterization of compact sets in the space is derived and some functionals on the space are discussed. We then proceed to prove some properties of probability measures on the space of measurable functions. After investigating conditions on function spaces which guarantee that weak convergence may be proved by establishing finite-dimensional convergence and tightness, we prove necessary and sufficient conditions for convergence in law of measurable processes. These results are then applied to convergence of the prediction process; a special case where the given process is Markov is studied in detail. We also derive two results on the prediction process which is not in the field of weak convergence. One is on the asymptotic behavior of the prediction process under absolutely continuity, and the other is an example which shows that the prediction process may lost Markov property if one uses a larger filtration than the natural one.
Book Synopsis Weak Convergence and Empirical Processes by : A. W. van der Vaart
Download or read book Weak Convergence and Empirical Processes written by A. W. van der Vaart and published by Springer Nature. This book was released on 2023-07-11 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an account of weak convergence theory, empirical processes, and their application to a wide variety of problems in statistics. The first part of the book presents a thorough treatment of stochastic convergence in its various forms. Part 2 brings together the theory of empirical processes in a form accessible to statisticians and probabilists. In Part 3, the authors cover a range of applications in statistics including rates of convergence of estimators; limit theorems for M− and Z−estimators; the bootstrap; the functional delta-method and semiparametric estimation. Most of the chapters conclude with “problems and complements.” Some of these are exercises to help the reader’s understanding of the material, whereas others are intended to supplement the text. This second edition includes many of the new developments in the field since publication of the first edition in 1996: Glivenko-Cantelli preservation theorems; new bounds on expectations of suprema of empirical processes; new bounds on covering numbers for various function classes; generic chaining; definitive versions of concentration bounds; and new applications in statistics including penalized M-estimation, the lasso, classification, and support vector machines. The approximately 200 additional pages also round out classical subjects, including chapters on weak convergence in Skorokhod space, on stable convergence, and on processes based on pseudo-observations.
Book Synopsis Weak Convergence of Financial Markets by : Jean-Luc Prigent
Download or read book Weak Convergence of Financial Markets written by Jean-Luc Prigent and published by Springer Science & Business Media. This book was released on 2003-05-19 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. The main problems, which include portfolio optimization, option pricing and hedging are examined, especially when considering discrete-time approximations of continuous-time dynamics. The third part deals with lattice- and tree-based computational procedures for option pricing both on stocks and stochastic bonds. More general discrete approximations are also introduced and detailed. Includes detailed examples.
Book Synopsis A Weak Convergence Approach to the Theory of Large Deviations by : Paul Dupuis
Download or read book A Weak Convergence Approach to the Theory of Large Deviations written by Paul Dupuis and published by John Wiley & Sons. This book was released on 1997-02-27 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applies the well-developed tools of the theory of weak convergenceof probability measures to large deviation analysis--a consistentnew approach The theory of large deviations, one of the most dynamic topics inprobability today, studies rare events in stochastic systems. Thenonlinear nature of the theory contributes both to its richness anddifficulty. This innovative text demonstrates how to employ thewell-established linear techniques of weak convergence theory toprove large deviation results. Beginning with a step-by-stepdevelopment of the approach, the book skillfully guides readersthrough models of increasing complexity covering a wide variety ofrandom variable-level and process-level problems. Representationformulas for large deviation-type expectations are a key tool andare developed systematically for discrete-time problems. Accessible to anyone who has a knowledge of measure theory andmeasure-theoretic probability, A Weak Convergence Approach to theTheory of Large Deviations is important reading for both studentsand researchers.
Book Synopsis Weak Convergence and the General Theory of Processes by : David J. Aldous
Download or read book Weak Convergence and the General Theory of Processes written by David J. Aldous and published by . This book was released on 1981 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Weak Convergence and Averaging for ODE. by :
Download or read book Weak Convergence and Averaging for ODE. written by and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Measure Theory by : Vladimir I. Bogachev
Download or read book Measure Theory written by Vladimir I. Bogachev and published by Springer Science & Business Media. This book was released on 2007-01-15 with total page 1075 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.
Book Synopsis Uniformity in Weak Convergence, and Some Applications by : P. Brown
Download or read book Uniformity in Weak Convergence, and Some Applications written by P. Brown and published by . This book was released on 1969 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Weak Convergence Methods and Singularly Pertubed Stochastic Control and Filtering Problems by :
Download or read book Weak Convergence Methods and Singularly Pertubed Stochastic Control and Filtering Problems written by and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals by : B. Dacorogna
Download or read book Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals written by B. Dacorogna and published by Springer. This book was released on 2006-11-14 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Analysis of Partial Differential Equations by : Jacques Louis Lions
Download or read book Numerical Analysis of Partial Differential Equations written by Jacques Louis Lions and published by Springer Science & Business Media. This book was released on 2011-06-07 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: S. Albertoni: Alcuni metodi di calcolo nella teoria della diffusione dei neutroni.- I. Babuska: Optimization and numerical stability in computations.- J.H. Bramble: Error estimates in elliptic boundary value problems.- G. Capriz: The numerical approach to hydrodynamic problems.- A. Dou: Energy inequalities in an elastic cylinder.- T. Doupont: On the existence of an iterative method for the solution of elliptic difference equation with an improved work estimate.- J. Douglas, J.R. Cannon: The approximation of harmonic and parabolic functions of half-spaces from interior data.- B.E. Hubbard: Error estimates in the fixed Membrane problem.- K. Jorgens: Calculation of the spectrum of a Schrödinger operator.- A. Lasota: Contingent equations and boundary value problems.- J.L. Lions: Réduction à des problèmes du type Cauchy-Kowalewska.- J.L. Lions: Problèmes aux limites non homogènes à données irrégulières; une méthode d’approximation.- J.L. Lions: Remarques sur l’approximation régularisée de problèmes aux limites.- W.V. Petryshyn: On the approximation-solvability of nonlinear functional equations in normed linear spaces.- P.A. Raviart: Approximation des équations d’évolution par des méthodes variationnelles.- M. Sibony, H. Brezis: Méthodes d’approximation et d’itération pour les operateurs monotones.- V. Thomee: Some topics in stability theory for partial difference operators.
Book Synopsis Canadian Journal of Mathematics by :
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1973-02 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computation and Applied Mathematics by :
Download or read book Computation and Applied Mathematics written by and published by . This book was released on 1997 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
