Moderate Deviations for Time-varying Dynamic Systems Driven by Nonhomogeneous Markov Chains with Two-time Scales∗
نویسندگان
چکیده
Motivated by problems arising in time-dependent queues and dynamic systems with random environment, this work develops moderate deviations principles for dynamic systems driven by a fast-varying nonhomogeneous Markov chain in continuous time. A distinct feature is that the Markov chain is time dependent or inhomogeneous so are the dynamic systems. Under irreducibility of the nonhomogeneous Markov chain, moderate deviations of a nonhomogeneous functional are established first. With the help of a martingale problem formulation and a functional central limit theorem for the two-time-scale system, moderate deviations upper and lower bounds are obtained for the rapidly fluctuating Markovian systems. Then applications to dynamic systems modulated by a fast-varying Markov chain are examined.
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