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

作　　者：Dung Tien Nguyen 

机构地区：[1]Department of Mathematics,Wayne State University

出　　处：《Acta Mathematicae Applicatae Sinica》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

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.

关 键 词：Markov chain backward equation two-time scale asymptotic expansion 

分 类 号：O211.62[理学—概率论与数理统计] TN713[理学—数学]