M. Malyutov and T. Zhang

Limit Theorems for Additive Functions of SCOT Trajectories

Stochastic COntext Tree (abbreviated as SCOT) is m-Markov Chain with every state of a string independent of the symbols in its more remote past than the context of length determined by the preceding symbols of this state. SCOT has also appeared in other fields under somewhat confusing names VLMC, PST, CTW,... for compression applications. SCOT modeling and its stationary distribution study was the subject of our preceding publication (IP, No. 3, 2014). We estimated SCOT parameters and tested homogeneity of data strings using additive functions of SCOT trajectories in IP, No. 4, 2013. Here we justify properties of the homogeneity test statistic introduced there and for finding active inputs of sparse systems with correlated noise.

КЛЮЧЕВЫЕ СЛОВА: variable length Markov chain, stochastic context Tree, asymptotic normality, additive functions of SCOT trajectories, large deviations