Probability Theory and Stochastic Modelling

Stochastic Optimal Control in Infinite Dimension

Dynamic Programming and HJB Equations

Authors: Fabbri, Giorgio, Gozzi, Fausto, Swiech, Andrzej

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  • 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
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eBook $169.00
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  • ISBN 978-3-319-53067-3
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Hardcover $219.99
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  • ISBN 978-3-319-53066-6
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Softcover $219.99
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  • ISBN 978-3-319-85053-5
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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.


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.


Reviews

“This book addresses a comprehensive study of the theory of stochastic optimal control when the underlying dynamic evolves as a stochastic differential equation in infinite dimension. It contains the most general models appearing in the literature and at the same time provides interesting applications. The book is well written and is mainly addressed to graduate students of engineering and of pure and applied mathematics.” (Hector Jasso, zbMATH 1379.93001, 2018)

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $169.00
price for USA in USD (gross)
  • ISBN 978-3-319-53067-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $219.99
price for USA in USD
  • ISBN 978-3-319-53066-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $219.99
price for USA in USD
  • ISBN 978-3-319-85053-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Stochastic Optimal Control in Infinite Dimension
Book Subtitle
Dynamic Programming and HJB Equations
Authors
Series Title
Probability Theory and Stochastic Modelling
Series Volume
82
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-53067-3
DOI
10.1007/978-3-319-53067-3
Hardcover ISBN
978-3-319-53066-6
Softcover ISBN
978-3-319-85053-5
Series ISSN
2199-3130
Edition Number
1
Number of Pages
XXIV, 916
Topics