Wroclaw University of Economics and Business

output

19932023

most citedArtificial Intelligence Technologies in Education: Benefits, Challenges and Strategies of Implementation

220 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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3 papers · 1 filter

math.PR2018★ 21 cited

Sojourn times of Gaussian processes with trend

Krzysztof Debicki, Peng Liu, Zbigniew Michna

We derive exact tail asymptotics of sojourn time above the level $u \geq 0$ $P (v (u) \int_{0}^{T} I (X (t) - c t > u) d t > x), x \geq 0$ as $u \to \infty$ , wher…

math.PR2016★ 8 cited

A Characterization of the Normal Distribution by the Independence of a Pair of Random Vectors

Wiktor Ejsmont

Kagan and Shalaevski 1967 have shown that if the random variables $X_{1}, \dots, X_{n}$ are independent and identically distributed and the distribution of $\sum_{i = 1}^{n} (X_{i} + a_{i})^{2}$ $a_i…

math.PR2012

Explicit formula for the supremum distribution of a spectrally negative stable process

Zbigniew Michna

In this article we get simple explicit formulas for $\Exp\sup_{s\leq t}X(s)$ where $X$ is a spectrally positive or negative Lévy process with infinite variation. As a consequence w…