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Asymptotic Expansions of Backward Equations for Two-time-scale Markov Chains in Continuous Time

Asymptotic Expansions of Backward Equations for Two-time-scale Markov Chains in Continuous Time
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摘要 This work develops asymptotic expansions for solutions of systems of backward equations of time- inhomogeneous Maxkov chains in continuous time. Owing to the rapid progress in technology and the increasing complexity in modeling, the underlying Maxkov chains often have large state spaces, which make the computa- tional tasks ihfeasible. To reduce the complexity, two-time-scale formulations are used. By introducing a small parameter ε〉 0 and using suitable decomposition and aggregation procedures, it is formulated as a singular perturbation problem. Both Markov chains having recurrent states only and Maxkov chains including also tran- sient states are treated. Under certain weak irreducibility and smoothness conditions of the generators, the desired asymptotic expansions axe constructed. Then error bounds are obtained. This work develops asymptotic expansions for solutions of systems of backward equations of time- inhomogeneous Maxkov chains in continuous time. Owing to the rapid progress in technology and the increasing complexity in modeling, the underlying Maxkov chains often have large state spaces, which make the computa- tional tasks ihfeasible. To reduce the complexity, two-time-scale formulations are used. By introducing a small parameter ε〉 0 and using suitable decomposition and aggregation procedures, it is formulated as a singular perturbation problem. Both Markov chains having recurrent states only and Maxkov chains including also tran- sient states are treated. Under certain weak irreducibility and smoothness conditions of the generators, the desired asymptotic expansions axe constructed. Then error bounds are obtained.
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2009年第3期457-476,共20页 应用数学学报(英文版)
基金 supported in part by the National Science Foundation under DMS-0603287 inpart by the National Security Agency under grant MSPF-068-029 in part by the National Natural ScienceFoundation of China(No.70871055) supported in part by Wayne State University under Graduate ResearchAssistantship
关键词 Markov chain backward equation two-time scale asymptotic expansion Markov chain backward equation two-time scale asymptotic expansion
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参考文献18

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