Stochastic Equations in Infinite Dimensions (Encyclopedia of Mathematics and its Applications, Series Number 45)

The aim of this book is to give a systematic and self-contained presentation of the basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Itô and Gikhman that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measures on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof.

Reference

Zabczyk, Jerzy

Da Prato, Guiseppe

Encyclopedias & Subject Guides

Cambridge University Press

Mathematical Control Theory: An Introduction presents, in a mathematically precise manner, a unified introduction to deterministic control theory. In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. "Covers a remarkable number of topics . . . The book presents a large amount of material very well, and its use is highly recommended." --Bulletin of the AMS

Mathematical Control Theory: An Introduction (Modern Birkhäuser Classics)

Birkhauser

Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. In the first part the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. This revised edition includes two brand new chapters surveying recent developments in the area and an even more comprehensive bibliography, making this book an essential and up-to-date resource for all those working in stochastic differential equations.

Stochastic Equations in Infinite Dimensions (Encyclopedia of Mathematics and its Applications, Series Number 152)

Science & Math

Da Prato, Giuseppe

Mathematics

Mathematical models of bond markets are of interest to researchers working in applied mathematics, especially in mathematical finance. This book concerns bond market models in which random elements are represented by Lévy processes. These are more flexible than classical models and are well suited to describing prices quoted in a discontinuous fashion. The book's key aims are to characterize bond markets that are free of arbitrage and to analyze their completeness. Nonlinear stochastic partial differential equations (SPDEs) are an important tool in the analysis. The authors begin with a relatively elementary analysis in discrete time, suitable for readers who are not familiar with finance or continuous time stochastic analysis. The book should be of interest to mathematicians, in particular to probabilists, who wish to learn the theory of the bond market and to be exposed to attractive open mathematical problems.

Mathematics of the Bond Market: A Lévy Processes Approach (Encyclopedia of Mathematics and its Applications, Series Number 174)

Barski, Michał

This textbook presents, in a mathematically precise manner, a unified introduction to deterministic control theory. With the exception of a few more advanced concepts required for the final part of the book, the presentation requires only a knowledge of basic facts from linear algebra, differential equations, and calculus. 
In addition to classical concepts and ideas, the author covers the stabilization of nonlinear systems using topological methods, realization theory for nonlinear systems, impulsive control and positive systems, the control of rigid bodies, the stabilization of infinite dimensional systems, and the solution of minimum energy problems. 
This second edition includes new chapters that introduce a variety of topics, such as controllability with vanishing energy, boundary control systems, and delayed systems. With additional proofs, theorems, results, and a substantially larger index, this new edition will be an invaluable resource for students and researchers of control theory. 
Mathematical Control Theory: An Introduction will be ideal for a beginning graduate course in mathematical control theory, or for self-study by professionals needing a complete picture of the mathematical theory that underlies the applications of control theory. 
From reviews of the first edition: 
At last! We did need an introductory textbook on control which can be read, understood, and enjoyed by anyone. Gian-Carlo Rota, The Bulletin of Mathematics Books 
It covers a remarkable number of topics...The exposition is excellent, and the book is a joy to read. A novel one-semester course covering both linear and nonlinear systems could be given...The book is an excellent one for introducing a mathematician to control theory. Bulletin of the AMS 
Indeed, for mathematicians who look for the basic ideas or a general picture about the main branches of control theory, I believe this book can provide an excellent bridge to this area. IEEE Control Systems Magazine

Mathematical Control Theory: An Introduction (Systems & Control: Foundations & Applications)

Mathematical control theory is a separate branch of mathematics that has, over a span of 150 years, developed an extensive literature covering its various ideas and applications. This text presents basic concepts and results in the field. It requires only a knowledge of basic facts from linear algebra, differential equations and calculus, with a few more concepts required for the final part of the book. In addition to classical concepts and ideas, the book presents many recently published results. It explains impulsive control, positive systems, stabilization of nonlinear systems, control of rigid bodies, stabilization of infinite dimensional systems and the minimum energy problem. The book should be useful for a beginning graduate course in mathematical control theory or for self study by professionals needing a complete picture of the mathematics that underly the applications of control theory.

Mathematical control theory: An introduction (Systems & control)

Mathematical theory of discrete time decision processes, also known as stochastic control, is based on two major ideas: backward induction and conditioning. It has a large number of applications in almost all branches of the natural sciences. The aim of these notes is to give a self-contained introduction to this theory and its applications. Our intention was to give a global and mathematically precise picture of the subject and present well motivated examples. We cover systems with complete or partial information as well as with complete or partial observation. We have tried to present in a unified way several topics such as dynamic programming equations, stopping problems, stabilization, Kalman-Bucy filter, linear regulator, adaptive control and option pricing. The notes discuss a large variety of models rather than concentrate on general existence theorems.

Chance and decision. Stochastic control in discrete time (Publications of the Scuola Normale Superiore)

Edizioni della Normale

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Books by Zabczyk, Jerzy

See the best price to sell, buy, or rent books by Zabczyk, Jerzy. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Stochastic Equations in Infinite Dimensions (Encyclopedia of Mathematics and its Applications, Series Number 45)

Stochastic Equations in Infinite Dimensions (Encyclopedia of Mathematics and its Applications, Series Number 45)

Mathematical Control Theory: An Introduction (Modern Birkhäuser Classics)

Stochastic Equations in Infinite Dimensions (Encyclopedia of Mathematics and its Applications, Series Number 152)

Mathematics of the Bond Market: A Lévy Processes Approach (Encyclopedia of Mathematics and its Applications, Series Number 174)

Mathematical Control Theory: An Introduction (Systems & Control: Foundations & Applications)

Mathematical control theory: An introduction (Systems & control)

Chance and decision. Stochastic control in discrete time (Publications of the Scuola Normale Superiore)