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Titlebook: Stochastic Optimal Control in Infinite Dimension; Dynamic Programming Giorgio Fabbri,Fausto Gozzi,Andrzej ?wi?ch Book 2017 Springer Intern

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發(fā)表于 2025-3-21 17:33:13 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Stochastic Optimal Control in Infinite Dimension
副標(biāo)題Dynamic Programming
編輯Giorgio Fabbri,Fausto Gozzi,Andrzej ?wi?ch
視頻videohttp://file.papertrans.cn/879/878053/878053.mp4
概述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 i
叢書名稱Probability Theory and Stochastic Modelling
圖書封面Titlebook: Stochastic Optimal Control in Infinite Dimension; Dynamic Programming Giorgio Fabbri,Fausto Gozzi,Andrzej ?wi?ch Book 2017 Springer Intern
描述.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 ope
出版日期Book 2017
關(guān)鍵詞49Lxx, 93E20, 49L20, 35R15, 35Q93, 49L25, 65H15, 37L55; stochastic optimal control; infinite dimension
版次1
doihttps://doi.org/10.1007/978-3-319-53067-3
isbn_softcover978-3-319-85053-5
isbn_ebook978-3-319-53067-3Series ISSN 2199-3130 Series E-ISSN 2199-3149
issn_series 2199-3130
copyrightSpringer International Publishing AG 2017
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沙發(fā)
發(fā)表于 2025-3-21 22:03:40 | 只看該作者
板凳
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Mild Solutions in Spaces of Continuous Functions, Hilbert spaces through a . which was first introduced in [147, 340] and then improved and developed in various subsequent papers like [89, 90, 306, 307, 317] and later [105, 107, 301, 309, 310, 431–434].
地板
發(fā)表于 2025-3-22 05:33:48 | 只看該作者
Preliminaries on Stochastic Calculus in Infinite Dimension,We recall some basic notions of measure theory and give a short introduction to random variables and the theory of the Bochner integral.
5#
發(fā)表于 2025-3-22 08:54:44 | 只看該作者
Optimal Control Problems and Examples,In this chapter we discuss the connection between the study of infinite-dimensional stochastic optimal control problems and that of second-order Hamilton–Jacobi–Bellman (HJB) equations in Hilbert spaces.
6#
發(fā)表于 2025-3-22 13:48:59 | 只看該作者
Viscosity Solutions,This chapter is devoted to the theory of viscosity solutions of Hamilton–Jacobi–Bellman equations in Hilbert spaces.
7#
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8#
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HJB Equations Through Backward Stochastic Differential Equations,This last chapter of the book completes the picture of the main methods used to study second-order HJB equations in Hilbert spaces and related optimal control problems by presenting a survey of results that can be achieved with the techniques of Backward SDEs in infinite dimension.
9#
發(fā)表于 2025-3-23 01:27:49 | 只看該作者
Giorgio Fabbri,Fausto Gozzi,Andrzej ?wi?chProvides 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 i
10#
發(fā)表于 2025-3-23 09:17:58 | 只看該作者
978-3-319-85053-5Springer International Publishing AG 2017
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