Overview
- Provides a systematic survey of the main available results, with proofs and references
- Gives a complete presentation of the theory of regular and viscosity solutions of second-order HJB equations in infinite-dimensional Hilbert spaces
- Reviews alternative approaches to the theory
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 82)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs,and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Reviews
Authors and Affiliations
About the authors
Giorgio Fabbri is a CNRS Researcher at the Aix-Marseille School of Economics, Marseille, France. He works on optimal control of deterministic and stochastic systems, notably in infinite dimensions, with applications to economics. He has also published various papers in several economic areas, in particular in growth theory and development economics.
Fausto Gozzi is a Full Professor of Mathematics for Economics and Finance at Luiss University, Roma, Italy. His main research field is the optimal control of finite and infinite-dimensional systems and its economic and financial applications. He is the author of many papers in various subjects areas, from Mathematics, to Economics and Finance.
Andrzej Swiech is a Full Professor at the School of Mathematics, Georgia Institute of Technology, Atlanta, USA. He received Ph.D. from UCSB in 1993. His main research interests are in nonlinear PDEs and integro-PDEs, PDEs in infinite dimensional spaces, viscosity solutions, stochastic and deterministic optimal control, stochastic PDEs, differential games, mean-field games, and the calculus of variations.*Marco Fuhrman* is a Full Professor of Probability and Mathematical Statistics at the University of Milano, Italy. His main research topics are stochastic differential equations in infinite dimensions and backward stochastic differential equations for optimal control of stochastic processes.
*Gianmario Tessitore* is a Full Professor of Probability and Mathematical Statistics at Milano-Bicocca University. He is the author of several scientific papers on control of stochastic differential equations in finite and infinite dimensions. He is, in particular, interested in the applications of backward stochastic differential equations in stochastic control.
Bibliographic Information
Book Title: Stochastic Optimal Control in Infinite Dimension
Book Subtitle: Dynamic Programming and HJB Equations
Authors: Giorgio Fabbri, Fausto Gozzi, Andrzej Święch
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-319-53067-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-53066-6Published: 07 July 2017
Softcover ISBN: 978-3-319-85053-5Published: 09 September 2018
eBook ISBN: 978-3-319-53067-3Published: 22 June 2017
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XXIV, 916
Topics: Calculus of Variations and Optimal Control; Optimization, Probability Theory and Stochastic Processes, Partial Differential Equations, Systems Theory, Control, Functional Analysis