Probability and Mathematical Statistics, 34, z. 2, 2014

Asymptotic results for random polynomials on the unit circle

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Random polynomials, Brownian bridge, stochastic process

On dual generators for non-local semi-Dirichlet forms

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Semi-Dirichlet form, non-local operator, stable-like process

A unified weighted family of distributions which contains the skew-elliptical family

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Multivariate weighted normal distribution, unified weighted family of distributions, skew-elliptical family

The limiting behaviour of sums and maximums of iid random variables from the viewpoint of different observers

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Central limit theorem, extreme value theory, observed and unobserved random variables

Refined solutions of time inhomogeneous optimal stopping problem and zero-sum game via Dirichlet form

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Time inhomogeneous Dirichlet form, optimal stopping, zero-sum game, variational inequality

A note on preservation of the generalized TTT transform order

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Total time on test transform, dispersive order, convex order, stochastic order, mixture, IFR

Bargmann measures for t-deformed probability

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Bargmann representation, deformation, complex moment problem

Persistence of some iterated processes

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Iterated process, one-sided barrier problem, one-sided exit problem, persistence, persistence probability, small deviation probability, survival probability

Data driven tests for univariate symmetry about an unknown median

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Testing symmetry, unknown center of symmetry, data driven score test, effective score, Schwarz type rule, model selection, rank test, kernel estimation, robust estimation, Monte Carlo study

The quantum decomposition associated with the Lévy white noise processes without moments

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Quantum decomposition, Kolmogorov representation, Lévy white noise processes, Araki–Woods–Parthasarathy– Schmidt characterization

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