Stability of Markov processes nonhomogeneous in time

Marta Tyran-Kamińska

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Large deviations and full Edgeworth expansions for finite Markov chains with applications to the analysis of genomic sequences

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To establish lists of words with unexpected frequencies in long sequences, for instance in a molecular biology context, one needs to quantify the exceptionality of families of word frequencies in random sequences. To this aim, we study large deviation probabilities of multidimensional word counts for Markov and hidden Markov models. More specifically, we compute local Edgeworth expansions of arbitrary degrees for multivariate partial sums of lattice valued functionals of finite...