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.

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 Levy 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.

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

The meeting intended to continue the traditional line of the foregoing conferences and to focus on topics of present research in the field of stochastic systems and optimization. Particular emphasis was placed on stochastic differential systems both finite and infinite dimensional, filtering, stochastic control, asymptotic methods and periodic systems.

Second order linear parabolic and elliptic equations arise frequently in mathematical physics, biology and finance. Here the authors present a state of the art treatment of the subject from a new perspective. They then go on to discuss how the results in the book can be applied to control theory. This area is developing rapidly and there are numerous notes and references that point the reader to more specialized results not covered in the book. Coverage of some essential background material helps to make the book self contained.

The notes are based on lectures on stochastic processes given at Scuola Normale Superiore in 1999 and 2000. Some new material was added and only selected, less standard results were presented. We did not include several applications to statistical mechanics and mathematical finance, covered in the lectures, as we hope to write part two of the notes devoted to applications of stochastic processes in modelling. The main themes of the notes are constructions of stochastic processes. We present different approaches to the existence question proposed by Kolmogorov, Wiener, Ito and Prohorov. Special attention is also paid to Levy processes. The lectures are basically self-contained and rely only on elementary measure theory and functional analysis. They might be used for more advanced courses on stochastic processes.

The theory of adaptive control is concerned with construction of strategies so that the controlled system behaves in a desirable way, without assuming the complete knowledge of the system. The models considered in this comprehensive book are of Markovian type. Both partial observation and partial information cases are analyzed. While the book focuses on discrete time models, continuous time ones are considered in the final chapter. The book provides a novel perspective by summarizing results on adaptive control obtained in the Soviet Union, which are not well known in the West. Comments on the interplay between the Russian and Western methods are also included.