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General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions

2014-06-02 Science
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Release : 2014-06-02
Genre : Science
Kind : eBook
Book Rating : 323/5 ( reviews)

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Book Synopsis General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions by : Qi Lü

Download or read book General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions written by Qi Lü. This book was released on 2014-06-02. Available in PDF, EPUB and Kindle. Book excerpt: The classical Pontryagin maximum principle (addressed to deterministic finite dimensional control systems) is one of the three milestones in modern control theory. The corresponding theory is by now well-developed in the deterministic infinite dimensional setting and for the stochastic differential equations. However, very little is known about the same problem but for controlled stochastic (infinite dimensional) evolution equations when the diffusion term contains the control variables and the control domains are allowed to be non-convex. Indeed, it is one of the longstanding unsolved problems in stochastic control theory to establish the Pontryagin type maximum principle for this kind of general control systems: this book aims to give a solution to this problem. This book will be useful for both beginners and experts who are interested in optimal control theory for stochastic evolution equations.

Backward Stochastic Evolution Equations in Infinite Dimensions

2013
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Release : 2013
Genre :
Kind : eBook
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Book Synopsis Backward Stochastic Evolution Equations in Infinite Dimensions by : Abdul Rahman Al-Hussein

Download or read book Backward Stochastic Evolution Equations in Infinite Dimensions written by Abdul Rahman Al-Hussein. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt:

General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions

2014-06-30
Download General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions PDF Online Free

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Release : 2014-06-30
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Kind : eBook
Book Rating : 332/5 ( reviews)

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Book Synopsis General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions by : Qi Lu

Download or read book General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions written by Qi Lu. This book was released on 2014-06-30. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Control Theory for Stochastic Partial Differential Equations

2021-10-19 Science
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Release : 2021-10-19
Genre : Science
Kind : eBook
Book Rating : 318/5 ( reviews)

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Book Synopsis Mathematical Control Theory for Stochastic Partial Differential Equations by : Qi Lü

Download or read book Mathematical Control Theory for Stochastic Partial Differential Equations written by Qi Lü. This book was released on 2021-10-19. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.

Stochastic Equations in Infinite Dimensions

2014-04-17 Mathematics
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Release : 2014-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 153/5 ( reviews)

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Book Synopsis Stochastic Equations in Infinite Dimensions by : Giuseppe Da Prato

Download or read book Stochastic Equations in Infinite Dimensions written by Giuseppe Da Prato. This book was released on 2014-04-17. Available in PDF, EPUB and Kindle. Book excerpt: Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. In the first part the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. This revised edition includes two brand new chapters surveying recent developments in the area and an even more comprehensive bibliography, making this book an essential and up-to-date resource for all those working in stochastic differential equations.

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