This unified, revised second edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite-dimensional systems. The original editions received outstanding reviews, yet this new edition is more concise and self-contained. New material has been added to reflect the growth in the field over the past decade. There is a unique chapter on semigroup theory of linear operators that brings together advanced concepts and techniques which are usually treated independently. The material on delay systems and structural operators has not yet appeared anywhere in book form.

Representation and Control of Infinite Dimensional Systems

Bensoussan, Alain

Da Prato, Giuseppe

Delfour, Michel C.

Mitter, Sanjoy K.

Reference

Birkhauser

"Based on the International Federatiojn for Information Processing WG 7.2 Conference, held recently in Pisa, Italy. Provides recent results as well as entirely new material on control theory and shape analysis. Written by leading authorities from various desciplines."

Partial Differential Equation Methods in Control and Shape Analysis

Science & Math

Mathematics

CRC Press, Inc.

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)

Zabczyk, Jerzy

Cambridge University Press

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)

Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.

Stochastic Porous Media Equations (Lecture Notes in Mathematics, 2163)

Barbu, Viorel

Röckner, Michael

Springer

This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.

Functional Analytic Methods for Evolution Equations (Lecture Notes in Mathematics, 1855)

Lasiecka, Irena

Kunstmann, Peer Christian

Lunardi, Alessandra

Schnaubelt, Roland

Weis, Lutz

Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.

An Introduction to Infinite-Dimensional Analysis (Universitext)

Experiments, Instruments & Measurement

Kolmogorov Equations for Stochastic PDEs gives an introduction to stochastic partial differential equations, such as reaction-diffusion, Burgers and 2D Navier-Stokes equations, perturbed by noise. It studies several properties of corresponding transition semigroups, such as Feller and strong Feller properties, irreducibility, existence and uniqueness of invariant measures. In addition, the transition semigroups are interpreted as generalized solutions of Kologorov equations.

Kolmogorov Equations for Stochastic PDEs (Advanced Courses in Mathematics - CRM Barcelona)

Computers & Technology

Computer Science

This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown from a series of courses delivered at the Scuola Normale Superiore di Pisa (and also at the Trento and Funchal Universities) and has been refined over several years of teaching experience in the subject. The lectures are addressed to a reader who is familiar with basic notions of measure theory and functional analysis. The first part is devoted to the Gaussian measure in a separable Hilbert space, the Malliavin derivative, the construction of the Brownian motion and Itô's formula. The second part deals with the differential stochastic equations and their connection with parabolic problems. The third part contains an introduction to the Malliavin calculus. Several applications are given, notably the Feynman-Kac, Girsanov and Clark-Ocone formulae, the Krylov-Bogoliubov and Von Neumann theorems.

Introduction to Stochastic Analysis and Malliavin Calculus (Publications of the Scuola Normale Superiore, 7)

Edizioni della Normale

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

Books by Da Prato, Giuseppe

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

Representation and Control of Infinite Dimensional Systems

Partial Differential Equation Methods in Control and Shape Analysis

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

Stochastic Equations in Infinite Dimensions (Encyclopedia of Mathematics and its Applications)

Stochastic Porous Media Equations (Lecture Notes in Mathematics, 2163)

Functional Analytic Methods for Evolution Equations (Lecture Notes in Mathematics, 1855)

An Introduction to Infinite-Dimensional Analysis (Universitext)

An Introduction to Infinite-Dimensional Analysis (Universitext)

Kolmogorov Equations for Stochastic PDEs (Advanced Courses in Mathematics - CRM Barcelona)

Introduction to Stochastic Analysis and Malliavin Calculus (Publications of the Scuola Normale Superiore, 7)