Probability and Mathematical Statistics, 35, z. 1, 2015, ss.178

On non-uniform Berry–Esseen bounds for time series

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Berry–Esseen, weak dependence

Innovation and factorization of the density of a regular PC sequence

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Periodically correlated sequence, prediction, innovation process, factorization of analytic vector functions

J-regularity of multivariate stationary sequences for some families J

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Multivariate stationary sequence, spectral density, J -regularity

Contractions and central extensions of Quantum White Noise Lie algebras

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Contraction of a Lie algebra, renormalized powers of quantum white noise, Virasoro algebra, W-algebras

The Fisher information and exponential families parametrized by a segment of means

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Fisher information, efficient estimator, exponential family, multivariate Gaussian distribution, Wishart distribution, parsimony

Refi ned data driven tests for univariate symmetry

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Testing symmetry, non-smooth functions, data driven score test, effective score, Schwarz-type rule, model selection, rank test, Monte Carlo study

J1 convergence of partial sum processes with a reduced number of jumps

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Functional limit theorem, partial sum process, regular variation, Skorokhod J1 topology, Lévy process, weak dependence, mixing

Almost sure limit points of lightly trimmed sums when the distribution function belongs to the domain of partial attraction of a positive semi-stable law

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Lightly trimmed sums, law of the iterated logarithm, semi-stable law, almost sure limit points

Captivity of mean-fi eld particle systems and the related exit problems

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Interacting particle system, propagation of chaos, exit time, nonconvexity, free energy, invariant probabilities

Small deviation probabilities of weighted sums with fast decreasing weights

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Small deviation probabilities, i.i.d. positive random variables, weighted sums, slowly varying functions, regularly varying functions.

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