Download or read book Vector Integration and Stochastic Integration in Banach Spaces written by Nicolae Dinculeanu and published by John Wiley & Sons. This book was released on 2011-09-28 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: A breakthrough approach to the theory and applications of stochastic integration The theory of stochastic integration has become an intensely studied topic in recent years, owing to its extraordinarily successful application to financial mathematics, stochastic differential equations, and more. This book features a new measure theoretic approach to stochastic integration, opening up the field for researchers in measure and integration theory, functional analysis, probability theory, and stochastic processes. World-famous expert on vector and stochastic integration in Banach spaces Nicolae Dinculeanu compiles and consolidates information from disparate journal articles-including his own results-presenting a comprehensive, up-to-date treatment of the theory in two major parts. He first develops a general integration theory, discussing vector integration with respect to measures with finite semivariation, then applies the theory to stochastic integration in Banach spaces. Vector Integration and Stochastic Integration in Banach Spaces goes far beyond the typical treatment of the scalar case given in other books on the subject. Along with such applications of the vector integration as the Reisz representation theorem and the Stieltjes integral for functions of one or two variables with finite semivariation, it explores the emergence of new classes of summable processes that make applications possible, including square integrable martingales in Hilbert spaces and processes with integrable variation or integrable semivariation in Banach spaces. Numerous references to existing results supplement this exciting, breakthrough work.
Download or read book Stochastic Integration in Banach Spaces written by Vidyadhar Mandrekar and published by Springer. This book was released on 2016-08-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups.
Download or read book Stochastic Integration written by Michel Metivier and published by Academic Press. This book was released on 2014-07-10 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Stochastic Integration focuses on the processes, methodologies, and approaches involved in stochastic integration. The publication first takes a look at the Ito formula, stochastic integral equations, and martingales and semimartingales. Discussions focus on Meyer process and decomposition theorem, inequalities, examples of stochastic differential equations, general stochastic integral equations, and applications of the Ito formula. The text then elaborates on stochastic measures, including stochastic measures and related integration and the Riesz representation theorem. The manuscript tackles the special features of infinite dimensional stochastic integration, as well as the isometric integral of a Hubert-valued square integrable martingale, cylindrical processes, and stochastic integral with respect to 2-cylindrical martingales with finite quadratic variation. The book is a valuable reference for mathematicians and researchers interested in stochastic integration.
Download or read book Vector and Operator Valued Measures and Applications written by Don H. Tucker and published by Academic Press. This book was released on 2014-05-10 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector and Operator Valued Measures and Applications is a collection of papers presented at the Symposium on Vector and Operator Valued Measures and Applications held in Alta, Utah, on August 7-12, 1972. The symposium provided a forum for discussing vector and operator valued measures and their applications to various areas such as stochastic integration, electrical engineering, control theory, and scattering theory. Comprised of 37 chapters, this volume begins by presenting two remarks related to the result due to Kolmogorov: the first is a theorem holding for nonnegative definite functions from T X T to C (where T is an arbitrary index set), and the second applies to separable Hausdorff spaces T, continuous nonnegative definite functions ? from T X T to C, and separable Hilbert spaces H. The reader is then introduced to the extremal structure of the range of a controlled vector measure ? with values in a Hausdorff locally convex space X over the field of reals; how the theory of vector measures is connected with the theory of compact and weakly compact mappings on certain function spaces; and Daniell and Daniell-Bochner type integrals. Subsequent chapters focus on the disintegration of measures and lifting; products of spectral measures; and mean convergence of martingales of Pettis integrable functions. This book should be of considerable use to workers in the field of mathematics.
Download or read book Analysis in Banach Spaces written by Tuomas Hytönen and published by Springer. This book was released on 2016-11-26 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem. Over the past fifteen years, motivated by regularity problems in evolution equations, there has been tremendous progress in the analysis of Banach space-valued functions and processes. The contents of this extensive and powerful toolbox have been mostly scattered around in research papers and lecture notes. Collecting this diverse body of material into a unified and accessible presentation fills a gap in the existing literature. The principal audience that we have in mind consists of researchers who need and use Analysis in Banach Spaces as a tool for studying problems in partial differential equations, harmonic analysis, and stochastic analysis. Self-contained and offering complete proofs, this work is accessible to graduate students and researchers with a background in functional analysis or related areas.
Download or read book STOCHASTIC INTEGRATION IN BANACH SPACES AND APPLICATIONS written by NADAV BERMAN and published by . This book was released on 1981 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of cylindrical stochastic process in Banach space
Download or read book Random and Vector Measures written by Malempati Madhusudana Rao and published by World Scientific. This book was released on 2012 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. This book analyzes several stationary aspects and related processes.
Download or read book Stochastic Analysis A Series of Lectures written by Robert C. Dalang and published by Birkhäuser. This book was released on 2015-07-28 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents in thirteen refereed survey articles an overview of modern activity in stochastic analysis, written by leading international experts. The topics addressed include stochastic fluid dynamics and regularization by noise of deterministic dynamical systems; stochastic partial differential equations driven by Gaussian or Lévy noise, including the relationship between parabolic equations and particle systems, and wave equations in a geometric framework; Malliavin calculus and applications to stochastic numerics; stochastic integration in Banach spaces; porous media-type equations; stochastic deformations of classical mechanics and Feynman integrals and stochastic differential equations with reflection. The articles are based on short courses given at the Centre Interfacultaire Bernoulli of the Ecole Polytechnique Fédérale de Lausanne, Switzerland, from January to June 2012. They offer a valuable resource not only for specialists, but also for other researchers and Ph.D. students in the fields of stochastic analysis and mathematical physics. Contributors: S. Albeverio M. Arnaudon V. Bally V. Barbu H. Bessaih Z. Brzeźniak K. Burdzy A.B. Cruzeiro F. Flandoli A. Kohatsu-Higa S. Mazzucchi C. Mueller J. van Neerven M. Ondreját S. Peszat M. Veraar L. Weis J.-C. Zambrini
Download or read book Hilbert And Banach Space valued Stochastic Processes written by Yuichiro Kakihara and published by World Scientific. This book was released on 2021-07-29 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a development of the book entitled Multidimensional Second Order Stochastic Processes. It provides a research expository treatment of infinite-dimensional stationary and nonstationary stochastic processes or time series, based on Hilbert and Banach space-valued second order random variables. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes as well as the stationary class. A new type of the Radon-Nikodým derivative of a Banach space-valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes.Emphasis is on the use of functional analysis and harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Generalizations are made to consider Banach space-valued stochastic processes to include processes of pth order for p ≥ 1. Readers may find that the covariance kernel is always emphasized and reveals another aspect of stochastic processes.This book is intended not only for probabilists and statisticians, but also for functional analysts and communication engineers.
Download or read book Handbook of Measure Theory written by E. Pap and published by Elsevier. This book was released on 2002-10-31 with total page 1633 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this Handbook is to survey measure theory with its many different branches and its relations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications which support the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the various areas they contain many special topics and challenging problems valuable for experts and rich sources of inspiration. Mathematicians from other areas as well as physicists, computer scientists, engineers and econometrists will find useful results and powerful methods for their research. The reader may find in the Handbook many close relations to other mathematical areas: real analysis, probability theory, statistics, ergodic theory, functional analysis, potential theory, topology, set theory, geometry, differential equations, optimization, variational analysis, decision making and others. The Handbook is a rich source of relevant references to articles, books and lecture notes and it contains for the reader's convenience an extensive subject and author index.
Download or read book Topics in Banach Space Integration written by Stefan Schwabik and published by World Scientific. This book was released on 2005 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relatively new concepts of the HenstockKurzweil and McShane integrals based on Riemann type sums are an interesting challenge in the study of integration of Banach space-valued functions. This timely book presents an overview of the concepts developed and results achieved during the past 15 years. The HenstockKurzweil and McShane integrals play the central role in the book. Various forms of the integration are introduced and compared from the viewpoint of their generality. Functional analysis is the main tool for presenting the theory of summation gauge integrals.
Download or read book The Bartle Dunford Schwartz Integral written by Thiruvaiyaru V. Panchapagesan and published by Springer Science & Business Media. This book was released on 2008-08-17 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a thorough and comprehensive treatise on vector measures, treating the vectorial Radon integration in detail. It explores an interplay between, on the one side, linear operators, transferring real (complex) functions onto elements of locally convex Hausdorff spaces, and vector-valued measures, on the other. The book contains not only a large amount of new material but also corrects various errors in well-known results available in the literature.
Download or read book Stochastic Integration in Banach Spaces and Applications to Parabolic Evolution Equations written by Mark Christiaan Veraar and published by . This book was released on 2006 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vector Measures Integration and Related Topics written by Guillermo Curbera and published by Springer Science & Business Media. This book was released on 2010-02-21 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of articles on the theme "vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in thearea and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, andfunctional analysis. The material is of interest to experts, young researchers and postgraduate students.
Download or read book Functional and Operatorial Statistics written by Sophie Dabo-Niang and published by Springer Science & Business Media. This book was released on 2008-05-21 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: An increasing number of statistical problems and methods involve infinite-dimensional aspects. This is due to the progress of technologies which allow us to store more and more information while modern instruments are able to collect data much more effectively due to their increasingly sophisticated design. This evolution directly concerns statisticians, who have to propose new methodologies while taking into account such high-dimensional data (e.g. continuous processes, functional data, etc.). The numerous applications (micro-arrays, paleo- ecological data, radar waveforms, spectrometric curves, speech recognition, continuous time series, 3-D images, etc.) in various fields (biology, econometrics, environmetrics, the food industry, medical sciences, paper industry, etc.) make researching this statistical topic very worthwhile. This book gathers important contributions on the functional and operatorial statistics fields.
Download or read book Stochastic Integration and Generalized Martingales written by A. U. Kussmaul and published by Pitman Publishing. This book was released on 1977 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Integration in Banach Spaces written by Vidyadhar Mandrekar and published by Springer. This book was released on 2014-12-03 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for modeling the states of complex systems perturbed by random sources over time, such as interest rates in financial markets or temperature distributions in a specific region. It studies properties of the solutions of the stochastic equations, observing the long-term behavior and the sensitivity of the solutions to changes in the initial data. The authors consider an integration theory of measurable and adapted processes in appropriate Banach spaces as well as the non-Gaussian case, whereas most of the literature only focuses on predictable settings in Hilbert spaces. The book is intended for graduate students and researchers in stochastic (partial) differential equations, mathematical finance and non-linear filtering and assumes a knowledge of the required integration theory, existence and uniqueness results and stability theory. The results will be of particular interest to natural scientists and the finance community. Readers should ideally be familiar with stochastic processes and probability theory in general, as well as functional analysis and in particular the theory of operator semigroups.