Finite Approximations in Discrete-Time Stochastic Control

Quantized Models and Asymptotic Optimality

Nonfiction, Science & Nature, Science, Other Sciences, System Theory, Mathematics, Calculus
Cover of the book Finite Approximations in Discrete-Time Stochastic Control by Naci Saldi, Tamás Linder, Serdar Yüksel, Springer International Publishing
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Author: Naci Saldi, Tamás Linder, Serdar Yüksel ISBN: 9783319790336
Publisher: Springer International Publishing Publication: May 11, 2018
Imprint: Birkhäuser Language: English
Author: Naci Saldi, Tamás Linder, Serdar Yüksel
ISBN: 9783319790336
Publisher: Springer International Publishing
Publication: May 11, 2018
Imprint: Birkhäuser
Language: English

In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. 

This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original models and the methods are general enough that researchers can build corresponding approximation results, typically with no additional assumptions.

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In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. 

This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original models and the methods are general enough that researchers can build corresponding approximation results, typically with no additional assumptions.

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