Stochastic Optimal Control in Infinite Dimension: Dynamic Programming and Hjb Equations
暫譯: 無窮維隨機最優控制：動態規劃與Hjb方程式
Fabbri, Giorgio, Gozzi, Fausto, Święch, Andrzej
- 出版商: Springer
- 出版日期: 2017-07-07
- 售價: $9,920
- 貴賓價: 9.5 折 $9,424
- 語言: 英文
- 頁數: 916
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 3319530666
- ISBN-13: 9783319530666
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相關分類:
工程數學 Engineering-mathematics
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相關主題
商品描述
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.
商品描述(中文翻譯)
本書提供了無限維隨機最優控制的介紹，完整闡述了無限維希爾伯特空間中二階HJB方程的理論，並著重於其在相關隨機最優控制問題中的應用。書中包含了對最優隨機控制的一般介紹，包括基本結果（例如動態規劃原則）及其證明，並提供了應用範例。對於希爾伯特空間中二階HJB方程的粘性解和正則解的現有理論進行了完整且最新的闡述，並廣泛調查了其他方法，附有完整的參考文獻。特別是第六章，由M. Fuhrman和G. Tessitore撰寫，調查了在無限維隨機控制中出現的HJB方程的正則解理論，通過反向隨機微分方程（BSDEs）進行探討。本書對於從事隨機偏微分方程控制理論及無限維偏微分方程的純研究和應用研究者均有興趣。來自其他領域的讀者若想學習基本理論也會覺得本書有用。先修知識包括：標準的泛函分析、算子半群理論及其在偏微分方程研究中的應用、對有限維隨機最優控制問題的動態規劃方法的基本了解，以及無限維空間中的隨機分析和隨機方程的基礎知識。
作者簡介
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.
作者簡介(中文翻譯)
**喬治奧·法布里**（Giorgio Fabbri）是法國馬賽艾克斯-馬賽經濟學院（Aix-Marseille School of Economics）的CNRS研究員。他的研究專注於確定性和隨機系統的最佳控制，特別是在無限維度中的應用，並且與經濟學有關。他還在多個經濟領域發表了各種論文，特別是在增長理論和發展經濟學方面。
**法烏斯托·戈齊**（Fausto Gozzi）是意大利羅馬路易斯大學（Luiss University）經濟與金融數學的全職教授。他的主要研究領域是有限和無限維系統的最佳控制及其在經濟和金融中的應用。他在數學、經濟學和金融等多個主題領域發表了許多論文。
**安德烈·斯維赫**（Andrzej Swiech）是美國喬治亞理工學院（Georgia Institute of Technology）數學學院的全職教授。他於1993年在加州大學聖巴巴拉分校（UCSB）獲得博士學位。他的主要研究興趣包括非線性偏微分方程（PDEs）和積分偏微分方程、無限維空間中的PDEs、粘性解、隨機和確定性最佳控制、隨機PDEs、微分博弈、均場博弈以及變分法。
**馬爾科·富爾曼**（Marco Fuhrman）是意大利米蘭大學（University of Milano）概率與數學統計的全職教授。他的主要研究主題是無限維度中的隨機微分方程和用於隨機過程最佳控制的反向隨機微分方程。
**詹馬里奧·泰西托雷**（Gianmario Tessitore）是米蘭比科卡大學（Milano-Bicocca University）概率與數學統計的全職教授。他是多篇關於有限和無限維隨機微分方程控制的科學論文的作者。他特別對反向隨機微分方程在隨機控制中的應用感興趣。
