Asymptotic expansions of backward equations for two-time-scale Markov chains in continuous time |
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Authors: | G Yin Dung Tien Nguyen |
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Institution: | (1) Department of Mathematics, Wayne State University, Detroit, Michigan 48202, USA |
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Abstract: | This work develops asymptotic expansions for solutions of systems of backward equations of time-inhomogeneous Markov chains
in continuous time. Owing to the rapid progress in technology and the increasing complexity in modeling, the underlying Markov
chains often have large state spaces, which make the computational tasks infeasible. To reduce the complexity, two-time-scale
formulations are used. By introducing a small parameter ɛ > 0 and using suitable decomposition and aggregation procedures, it is formulated as a singular perturbation problem. Both
Markov chains having recurrent states only and Markov chains including also transient states are treated. Under certain weak
irreducibility and smoothness conditions of the generators, the desired asymptotic expansions are constructed. Then error
bounds are obtained.
Research of this author was supported in part by Wayne State University under Graduate Research Assistantship. |
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Keywords: | Markov chain backward equation two-time scale asymptotic expansion |
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