Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations
Giorgio Fabbri (),
Fausto Gozzi and
Additional contact information
Andrzej Swiech: School of Mathematics - Georgia Institute of Technology - Georgia Institute of Technology (Georgia Tech)
Post-Print from HAL
Providing an introduction to stochastic optimal control in infinite dimensions, 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 will be of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimensions. 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 dimensions, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Keywords: Economie; quantitative (search for similar items in EconPapers)
Note: View the original document on HAL open archive server: https://hal-amu.archives-ouvertes.fr/hal-01505767
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10) Track citations by RSS feed
Published in Springer, 2017, Probability Theory and Stochastic Modelling, 978-3-319-53066-6
There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01505767
Access Statistics for this paper
More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().