Finite Approximations in Discrete-Time Stochastic Control

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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.
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.
Demonstrates how quantization can be used to systematically optimize decentralized stochastic control problems Explores network control applications Provides a framework for comparing approximation models

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Themen in »Finite Approximations in Discrete-Time Stochastic Control«

stochastic control decentralized stochastic control quantization numerical approximation finite state approximations Markov decision processes asymptotic optimality

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“The book is very well written, with focus on clarity … . material of this monograph is pretty advanced, the presentation style is very clear, compact and relatively easy to follow, but at the same time mathematically rigorous. The monograph is a good piece of work on a subject that attracts considerable attention. Both researchers and professionals in applied mathematics will find this book very useful. It can also be recommended as a valuable reference text in approximate dynamic programming.” (Dariusz Uciński, zbMATH 1471.93005, 2021)

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