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Random And Vector Measures
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Book Synopsis Random and Vector Measures by : Malempati Madhusudana Rao
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.
Book Synopsis Vector and Operator Valued Measures and Applications by : Don H. Tucker
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 474 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.
Book Synopsis Optimal Control of Dynamic Systems Driven by Vector Measures by : N. U. Ahmed
Download or read book Optimal Control of Dynamic Systems Driven by Vector Measures written by N. U. Ahmed and published by Springer Nature. This book was released on 2021-09-13 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Vector Measures, Integration and Related Topics by : Guillermo Curbera
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 Vector Measures written by Joseph Diestel and published by American Mathematical Soc.. This book was released on 1977-06-01 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this survey the authors endeavor to give a comprehensive examination of the theory of measures having values in Banach spaces. The interplay between topological and geometric properties of Banach spaces and the properties of measures having values in Banach spaces is the unifying theme. The first chapter deals with countably additive vector measures finitely additive vector measures, the Orlicz-Pettis theorem and its relatives. Chapter II concentrates on measurable vector valued functions and the Bochner integral. Chapter III begins the study of the interplay among the Radon-Nikodym theorem for vector measures, operators on $L_1$ and topological properties of Banach spaces. A variety of applications is given in the next chapter. Chapter V deals with martingales of Bochner integrable functions and their relation to dentable subsets of Banach spaces. Chapter VI is devoted to a measure-theoretic study of weakly compact absolutely summing and nuclear operators on spaces of continuous functions. In Chapter VII a detailed study of the geometry of Banach spaces with the Radon-Nikodym property is given. The next chapter deals with the use of Radon-Nikodym theorems in the study of tensor products of Banach spaces. The last chapter concludes the survey with a discussion of the Liapounoff convexity theorem and other geometric properties of the range of a vector measure. Accompanying each chapter is an extensive survey of the literature and open problems.
Download or read book Vector Measures written by Joe Diestel and published by . This book was released on 1979 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Random Probability Measures on Polish Spaces by : Hans Crauel
Download or read book Random Probability Measures on Polish Spaces written by Hans Crauel and published by CRC Press. This book was released on 2002-07-25 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph the narrow topology on random probability measures on Polish spaces is investigated in a thorough and comprehensive way. As a special feature, no additional assumptions on the probability space in the background, such as completeness or a countable generated algebra, are made. One of the main results is a direct proof of the rando
Book Synopsis Probability Theory on Vector Spaces III by : D Szynal
Download or read book Probability Theory on Vector Spaces III written by D Szynal and published by Springer. This book was released on 2006-12-08 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ind-additive Functionals on Random Vectors by : Wojbor Andrzej Woyczyński
Download or read book Ind-additive Functionals on Random Vectors written by Wojbor Andrzej Woyczyński and published by . This book was released on 1970 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Rings of Sets and the Theory of Vector Measures by : V. M. Bogdan
Download or read book Topological Rings of Sets and the Theory of Vector Measures written by V. M. Bogdan and published by . This book was released on 1978 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Generalized Functionals of Brownian Motion and Their Applications by : Nasir Uddin Ahmed
Download or read book Generalized Functionals of Brownian Motion and Their Applications written by Nasir Uddin Ahmed and published by World Scientific. This book was released on 2012 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process OCo covering the classical WienerOCoIto class including the generalized functionals of Hida as special cases, among others. It presents a thorough and comprehensive treatment of the WienerOCoSobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems. Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated RieszOCoFischer theorem for separable Hilbert spaces and the space of WienerOCoIto functionals is drawn out, thus providing a clear insight into the subject.
Book Synopsis Counterparty Credit Risk, Collateral and Funding by : Damiano Brigo
Download or read book Counterparty Credit Risk, Collateral and Funding written by Damiano Brigo and published by John Wiley & Sons. This book was released on 2013-04-22 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book's content is focused on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk. The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for counterparty credit and funding risk, inclusive of collateral, netting rules, possible debit valuation adjustments, re-hypothecation and closeout rules. The book however also looks at quite practical problems, linking particular models to particular 'concrete' financial situations across asset classes, including interest rates, FX, commodities, equity, credit itself, and the emerging asset class of longevity. The authors also aim to help quantitative analysts, traders, and anyone else needing to frame and price counterparty credit and funding risk, to develop a 'feel' for applying sophisticated mathematics and stochastic calculus to solve practical problems. The main models are illustrated from theoretical formulation to final implementation with calibration to market data, always keeping in mind the concrete questions being dealt with. The authors stress that each model is suited to different situations and products, pointing out that there does not exist a single model which is uniformly better than all the others, although the problems originated by counterparty credit and funding risk point in the direction of global valuation. Finally, proposals for restructuring counterparty credit risk, ranging from contingent credit default swaps to margin lending, are considered.
Book Synopsis Vector Space Measures and Applications II by : R.M. Aron
Download or read book Vector Space Measures and Applications II written by R.M. Aron and published by Springer. This book was released on 2006-11-15 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Random Measures, Theory and Applications by : Olav Kallenberg
Download or read book Random Measures, Theory and Applications written by Olav Kallenberg and published by Springer. This book was released on 2017-04-12 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Probability, Random Processes, and Ergodic Properties by : Robert M. Gray
Download or read book Probability, Random Processes, and Ergodic Properties written by Robert M. Gray and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been written for several reasons, not all of which are academic. This material was for many years the first half of a book in progress on information and ergodic theory. The intent was and is to provide a reasonably self-contained advanced treatment of measure theory, prob ability theory, and the theory of discrete time random processes with an emphasis on general alphabets and on ergodic and stationary properties of random processes that might be neither ergodic nor stationary. The intended audience was mathematically inc1ined engineering graduate students and visiting scholars who had not had formal courses in measure theoretic probability . Much of the material is familiar stuff for mathematicians, but many of the topics and results have not previously appeared in books. The original project grew too large and the first part contained much that would likely bore mathematicians and dis courage them from the second part. Hence I finally followed the suggestion to separate the material and split the project in two. The original justification for the present manuscript was the pragmatic one that it would be a shame to waste all the effort thus far expended. A more idealistic motivation was that the presentation bad merit as filling a unique, albeit smaIl, hole in the literature.
Book Synopsis Random Measures by : Olav Kallenberg
Download or read book Random Measures written by Olav Kallenberg and published by Academic Press. This book was released on 1983 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Acta Mathematica Vietnamica written by and published by . This book was released on 2001 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt:
