Stochastic Optimal Control in Infinite Dimension : Dynamic Programming and HJB Equations. 1st ed. 2017

種類:

電子ブック

責任表示:

by Giorgio Fabbri, Fausto Gozzi, Andrzej Święch

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Fabbri, Giorgio.
• Gozzi, Fausto.
• Święch, Andrzej.
• SpringerLink (Online service)

シリーズ名:

Probability Theory and Stochastic Modelling ; 82

ISBN:

9783319530673 [3319530674]    

注記:

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.
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

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