Physical Sciences and Mathematics Commons^™

Sequences Of Random Matrices Modulated By A Discrete-Time Markov Chain, Huy Nguyen

Wayne State University Dissertations

In this dissertation, we consider a number of matrix-valued random sequences that are modulated by a discrete-time Markov chain having a finite space.Assuming that the state space of the Markov chain is large, our main effort in this work is devoted to reducing the complexity. To achieve this goal, our formulation uses time-scale separation of the Markov chain. The state-space of the Markov chain is split into subspaces. Next, the states of the Markov chain in each subspace are aggregated into a ``super'' state. Then we normalize the matrix-valued sequences that are modulated by the two-time-scale Markov chain. Under simple …