Probability and Mathematical Statistics, 36, z. 1, 2016, ss.188

Extremes of chi-square processes with trend

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Chi-square process, Gaussian random field, safety region, tail asymptotics, first passage time, Pickands constant, Piterbarg constant, Fernique-type inequality

On the moment determinacy of products of non-identically distributed random variables

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Product of random variables, Stieltjes moment problem, Hamburger moment problem, Cramér’s condition, Carleman’s condition, Krein’s condition, Hardy’s condition

Cross-variation of Young integral with respect to long-memory fractional Brownian motions35

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Fractional Brownian motion, Rosenblatt process, Young integral, Breuer–Major theorem, Taqqu’s theorem, stochastic differential equations

On the order of approximation in the random central limit theorem for m-dependent random variables

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Random central limit theorem, m-dependent random variables, Berry–Esseen type bound, approximation

Existence of a persistent hub in the convex preferential attachment model

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Preferential attachment, persistent hub, Barabási–Albert model

Strong stationary duality for Möbius monotone Markov chains: Examples

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Markov chains, stochastic monotonicity, eigenvalues, Möbius monotonicity, strong stationary duality, strong stationary times, separation distance, mixing time, Ising model, hypercube

Sharp bounds for the bias of trimmed means of progressively censored order statistics

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Trimmed mean, progressive censoring, generalized order statistics, sharp bounds, bias

A limit process for a sequence of partial sums of residuals of a simple regression on order statistics with Markovmodulated noise

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Simple regression model, order statistics, Markov-modulated noise, regression residuals, empirical bridge

On the structure of a class of distributions obeying the principle of a single big jump

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Principle of a single big jump, strongly heavy-tailed distribution, weak tail equivalence, integrated tail distribution

A constant regression characterization of the Marchenko– Pastur law

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Lukacs characterization, free Poisson distribution, free cumulants

Sharp inequalities for the Haar system and martingale transforms

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Haar system, martingale, weak-type inequality, Bellman function, best constants

Kendall random walks

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Random walk, generalized convolution, weakly stable distribution, Kendall convolution, Pareto distribution, Markov process, Williamson transform

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