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    Reduction of Markov chains with two-time-scale state transitions

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    In this paper, we consider a general class of two-time-scale Markov chains whose transition rate matrix depends on a parameter Ξ»>0\lambda>0. We assume that some transition rates of the Markov chain will tend to infinity as Ξ»β†’βˆž\lambda\rightarrow\infty. We divide the state space of the Markov chain XX into a fast state space and a slow state space and define a reduced chain YY on the slow state space. Our main result is that the distribution of the original chain XX will converge in total variation distance to that of the reduced chain YY uniformly in time tt as Ξ»β†’βˆž\lambda\rightarrow\infty.Comment: 30 pages, 3 figures; Stochastics: An International Journal of Probability and Stochastic Processes, 201
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