A result concerning strongly erogodic nonhomogeneous Markov chains

Large Deviations for a Class of Nonhomogeneous Markov Chains

Large deviation results are given for a class of perturbed non-homogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {Pn} be a sequence of transition matrices on a finite state space which converge to a limit transition matrix P. Let {Xn} be the associated non-homogeneous Markov chain where Pn controls movement from ti...

Occupation laws for some time-nonhomogeneous Markov chains

We consider finite-state time-nonhomogeneous Markov chains whose transition matrix at time n is I + G/nζ where G is a “generator” matrix, that is G(i, j) > 0 for i, j distinct, and G(i, i) = − ∑ k 6=iG(i, k), and ζ > 0 is a strength parameter. In these chains, as time grows, the positions are less and less likely to change, and so form simple models of age-dependent time-reinforcing schemes. Th...

Dynamical properties of strongly interacting Markov chains

Spatial interdependences of multiple stochastic units can be suitably quantified by the Kullback-Leibler divergence of the joint probability distribution from the corresponding factorized distribution. In the present paper, a generalized measure for stochastic interaction, which also captures temporal interdependences, is analysed within the setting of Markov chains. The dynamical properties of...

Perfect Sampling for Nonhomogeneous Markov Chains and Hidden Markov Models By

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 e...