Displaying similar documents to “A tail inequality for suprema of unbounded empirical processes with applications to Markov chains.”

Infinite system of Brownian balls with interaction: the non-reversible case

Myriam Fradon, Sylvie Rœlly (2007)

ESAIM: Probability and Statistics

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We consider an infinite system of hard balls in d undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also show that Gibbs measures are reversible measures.

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

Pierre Pudlo (2010)

ESAIM: Probability and Statistics

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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...