A Class of Small Deviation Theorems for Random Sums of Multivariate Function of mth-order Markov Chain (pp. 63-77)
Kangkang Wang, De-Cai Zong · Azerbaijan Journal of Mathematics · 2012
In this paper, the notion of limit relative logarithmic likelihood ratio of stochasticsequence, as a measure of dissimilarity between the joint distribution and the mth-order nonhomogeneous Markov distribution, is introduced. A kind of strong limittheorems represented by inequalities which we call the small deviation theorems for thearbitrary stochastic sequence are obtained by constructing the consistent distributionfunctions. As corollaries, we obtain some small deviation theorems for the occurrencefrequency of the state groups and the harmonic mean of the transitional probabilitiesof the mth-order nonhomogeneous Markov chain.