Titlebook: Continuous-Time Markov Chains and Applications; A Singular Perturbat G. George Yin,Qing Zhang Book 19981st edition Springer Science+Busines

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https://doi.org/10.1007/978-3-322-95656-9This chapter is concerned with the analysis of the probability distributions of singularly perturbed Markov chains having weakly irreducible generators.

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https://doi.org/10.1007/978-3-322-95763-4Continuing the central themes of this book, as an application of the asymptotic properties of singularly perturbed Markov chains, this chapter focuses on hierarchical controls for a class of Markov decision problems. Our main attention is on finite-state continuous-time Markov decision processes (MDP) having weak and strong interactions.

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https://doi.org/10.1007/978-3-322-95789-4While Chapter 8 deals with Markov decision processes, this chapter is concerned with stochastic dynamical systems with the state . (.) ∈ ℝ. and the control satisfying.where ε > 0 is a small parameter, and α .(.), . ≥, is a Markov chain defined on a probability space (Ω., .) taking values in

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Asymptotic Expansion: Irreducible GeneratorsThis chapter is concerned with the analysis of the probability distributions of singularly perturbed Markov chains having weakly irreducible generators.

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Markov Decision ProblemsContinuing the central themes of this book, as an application of the asymptotic properties of singularly perturbed Markov chains, this chapter focuses on hierarchical controls for a class of Markov decision problems. Our main attention is on finite-state continuous-time Markov decision processes (MDP) having weak and strong interactions.

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https://doi.org/10.1007/978-3-322-95624-8singularly perturbed system involving two-time scales, namely, the actual time . and the stretched time ./ε To analyze such systems, one seeks to “average out” the fast variables and to consider only certain averaged characteristics via asymptotic methods.

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