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Autor: Giorgio Fabbri
ISBN-13: 9783319530673
Einband: eBook
Seiten: 916
Sprache: Englisch
eBook Typ: PDF
eBook Format: eBook
Kopierschutz: Adobe DRM [Hard-DRM]
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Stochastic Optimal Control in Infinite Dimension

82, Probability Theory and Stochastic Modelling
Dynamic Programming and HJB Equations
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1
Providing an introduction to stochastic optimal control in in?nite dimension, this book gives a complete account of the theory of second-order HJB equations in in?nite-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 in?nite-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 in?nite dimension. Readers from other ?elds who want to learn the basic theory will also ?nd 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 ?nite dimension, and the basics of stochastic analysis and stochastic equations in in?nite-dimensional spaces.
4
Preface.- 1.Preliminaries on stochastic calculus in infinite dimensions.- 2.Optimal control problems and examples.- 3.Viscosity solutions.- 4.Mild solutions in spaces of continuous functions.- 5.Mild solutions in L2 spaces.- 6.HJB Equations through Backward Stochastic Differential Equations (by M. Fuhrman and G. Tessitore).- Appendix A, B, C, D, E.- Bibliography.

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Autor: Giorgio Fabbri
ISBN-13 :: 9783319530673
ISBN: 3319530674
Verlag: Springer International Publishing
Seiten: 916
Sprache: Englisch
Auflage 1st ed. 2017
Sonstiges: Ebook