Random And Vector Measures
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Random And Vector Measures
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Author : M. M. Rao
language : en
Publisher: World Scientific
Release Date : 2011
Random And Vector Measures written by M. M. Rao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. The spaces can be Banach or Frechet types. Several stationary aspects and related processes are analyzed whilst numerous new results are included and many research avenues are opened up.
Random And Vector Measures
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Author : Malempati Madhusudana Rao
language : en
Publisher: World Scientific
Release Date : 2011-08-31
Random And Vector Measures written by Malempati Madhusudana Rao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-31 with Mathematics categories.
The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. The spaces can be Banach or Frechet types. Special attention is given to Bochner's boundedness principle and Grothendieck's representation unifying and simplyfying stochastic integrations. Several stationary aspects, extensions and random currents as well as related multilinear forms are analyzed, whilst numerous new procedures and results are included, and many research areas are opened up which also display the geometric aspects in multi dimensions.
Optimal Control Of Dynamic Systems Driven By Vector Measures
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Author : N. U. Ahmed
language : en
Publisher: Springer Nature
Release Date : 2021-09-13
Optimal Control Of Dynamic Systems Driven By Vector Measures written by N. U. Ahmed and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-13 with Mathematics categories.
This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions for optimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.
Vector Measures Integration And Related Topics
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Author : Guillermo Curbera
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-02-21
Vector Measures Integration And Related Topics written by Guillermo Curbera and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-21 with Mathematics categories.
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.
Random Measures Theory And Applications
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Author : Olav Kallenberg
language : en
Publisher: Springer
Release Date : 2017-04-12
Random Measures Theory And Applications written by Olav Kallenberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-12 with Mathematics categories.
Offering the first comprehensive treatment of the theory of random measures, this book has a very broad scope, ranging from basic properties of Poisson and related processes to the modern theories of convergence, stationarity, Palm measures, conditioning, and compensation. The three large final chapters focus on applications within the areas of stochastic geometry, excursion theory, and branching processes. Although this theory plays a fundamental role in most areas of modern probability, much of it, including the most basic material, has previously been available only in scores of journal articles. The book is primarily directed towards researchers and advanced graduate students in stochastic processes and related areas.
Integral Probability And Fractal Measures
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Author : Gerald A. Edgar
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Integral Probability And Fractal Measures written by Gerald A. Edgar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
This book may be considered a continuation of my Springer-Verlag text Mea sure, Topology, and Fractal Geometry. It presupposes some elementary knowl edge of fractal geometry and the mathematics behind fractal geometry. Such knowledge might be obtained by study of Measure, Topology, and Fractal Ge ometry or by study of one of the other mathematically oriented texts (such as [13] or [87]). I hope this book will be appropriate to mathematics students at the beginning graduate level in the U.S. Most references are numbered and may be found at the end of the book; but Measure, Topology, and Fractal Geometry is referred to as [ MTFG]. One of the reviews of [MTFG] says that it "sacrific[es] breadth of coverage 1 for systematic development" -although I did not have it so clearly formulated as that in my mind at the time I was writing the book, I think that remark is exactly on target. That sacrifice has been made in this volume as well. In many cases, I do not include the most general or most complete form of a result. Sometimes I have only an example of an important development. The goal was to omit most material that is too tedious or that requires too much background.
Gaussian Measures
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Author : Vladimir I. Bogachev
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-01-26
Gaussian Measures written by Vladimir I. Bogachev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-26 with Mathematics categories.
This book gives a systematic exposition of the modern theory of Gaussian measures. It presents with complete and detailed proofs fundamental facts about finite and infinite dimensional Gaussian distributions. Covered topics include linear properties, convexity, linear and nonlinear transformations, and applications to Gaussian and diffusion processes. Suitable for use as a graduate text and/or a reference work, this volume contains many examples, exercises, and an extensive bibliography. It brings together many results that have not appeared previously in book form.
Gaussian Measures In Hilbert Space
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Author : Alexander Kukush
language : en
Publisher: John Wiley & Sons
Release Date : 2020-02-26
Gaussian Measures In Hilbert Space written by Alexander Kukush and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-26 with Mathematics categories.
At the nexus of probability theory, geometry and statistics, a Gaussian measure is constructed on a Hilbert space in two ways: as a product measure and via a characteristic functional based on Minlos-Sazonov theorem. As such, it can be utilized for obtaining results for topological vector spaces. Gaussian Measures contains the proof for Ferniques theorem and its relation to exponential moments in Banach space. Furthermore, the fundamental Feldman-Hájek dichotomy for Gaussian measures in Hilbert space is investigated. Applications in statistics are also outlined. In addition to chapters devoted to measure theory, this book highlights problems related to Gaussian measures in Hilbert and Banach spaces. Borel probability measures are also addressed, with properties of characteristic functionals examined and a proof given based on the classical Banach Steinhaus theorem. Gaussian Measures is suitable for graduate students, plus advanced undergraduate students in mathematics and statistics. It is also of interest to students in related fields from other disciplines. Results are presented as lemmas, theorems and corollaries, while all statements are proven. Each subsection ends with teaching problems, and a separate chapter contains detailed solutions to all the problems. With its student-tested approach, this book is a superb introduction to the theory of Gaussian measures on infinite-dimensional spaces.
Fluid Mechanics Measurements
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Author : R. Goldstein
language : en
Publisher: Routledge
Release Date : 2017-11-13
Fluid Mechanics Measurements written by R. Goldstein and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-13 with Technology & Engineering categories.
This revised edition provides updated fluid mechanics measurement techniques as well as a comprehensive review of flow properties required for research, development, and application. Fluid-mechanics measurements in wind tunnel studies, aeroacoustics, and turbulent mixing layers, the theory of fluid mechanics, the application of the laws of fluid mechanics to measurement techniques, techniques of thermal anemometry, laser velocimetry, volume flow measurement techniques, and fluid mechanics measurement in non-Newtonian fluids, and various other techniques are discussed.
Fuzzy Sets Theory And Applications
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Author : André Jones
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fuzzy Sets Theory And Applications written by André Jones and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Problems in decision making and in other areas such as pattern recogni tion, control, structural engineering etc. involve numerous aspects of uncertainty. Additional vagueness is introduced as models become more complex but not necessarily more meaningful by the added details. During the last two decades one has become more and more aware of the fact that not all this uncertainty is of stochastic (random) cha racter and that, therefore, it can not be modelled appropriately by probability theory. This becomes the more obvious the more we want to represent formally human knowledge. As far as uncertain data are concerned, we have neither instru ments nor reasoning at our disposal as well defined and unquestionable as those used in the probability theory. This almost infallible do main is the result of a tremendous work by the whole scientific world. But when measures are dubious, bad or no longer possible and when we really have to make use of the richness of human reasoning in its variety, then the theories dealing with the treatment of uncertainty, some quite new and other ones older, provide the required complement, and fill in the gap left in the field of knowledge representation. Nowadays, various theories are widely used: fuzzy sets, belief function, the convenient associations between probability and fuzzines~ etc ••• We are more and more in need of a wide range of instruments and theories to build models that are more and more adapted to the most complex systems.