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Moderate deviations for time-varying dynamic systems driven by non-homogeneous Markov chains with Two-time Scales

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 non-homogeneous 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 non-homogeneous Markov chain, moderate deviations of a non-homogeneous functional are established first. With the help of a martingale problem formulation and a functional central limit theorem for the two timescale system, both upper and lower bounds of moderate deviations are obtained for the rapidly fluctuating Markovian systems. Then applications to queueing systems and dynamic systems modulated by a fast-varying Markov chain are examined.