Large deviations for a class of nonhomogeneous Markov chains: K-word level results

In previous work, Dietz and Sethuraman (2005), large deviations with respect to additive functionals were established for a class of finite-state time-nonhomogeneous Markov chains whose connecting transition matrices {Pn} converge to a general limit matrix P which includes some stochastic optimization algorithms. In this note, large deviations at the next level, that is with respect to K-word empirical measures for K ≥ 1, are established. The rate functions found connect the “K-word landscape” to features of the base convergence Pn → P in terms of an optimization over certain “routing” and “resting” costs which gives insight into how deviations are achieved. Research supported in part by NSA grant H982300510041.