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1

On extremal index of max-stable stationary processes

Dębicki K., Hashorva E.

Probability and Mathematical Statistics

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2017

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Vol. 37, Fasc. 2

299--317

EN

In this contribution we discuss the relation between Pickands-type constants defined for certain Brown-Resnick stationary proces W(t), t ϵ R, as [wzór] (set 0Z = R if δ = 0) and the extremal index of the associated max-stable stationary process ξW. We derive several new formulas and obtain lower bounds for ΉδW if W is a Gaussian or a Lévy process. As a by-product we show an interesting relation between Pickands constants and lower tail probabilities for fractional Brownian motions.

2

Ekologiczny przemysł

Dębicki K.

Inżynieria Bezwykopowa

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2014

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nr 3

66-68

PL

Wykonywanie prac budowlanych na obszarach szczególnie wrażliwych pod względem środowiska naturalnego wymaga zastosowania odpowiednich technologii. Dotyczy to również przewiertów HDD i co się z tym wiąże, właściwego doboru płynów wiertniczych.

3

Zielone przewierty HDD

Dębicki K.

Inżynieria Bezwykopowa

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2011

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nr 5

62-65

EN

Restrictions related to the EU directives on the emissions of greenhouse gases push the conventional energy sources into the background, thereby promoting the alternative ones. More and more hydro, solar and wind power plants are built. With shrinking place on the land, new projects are moved to the marine areas. That way, a project in the North Sea was created to group 21 wind farms. The way to deliver energy from the BorWin and DolWin areas is the route linking both locations with the northern coast of Germany. This involves crossing the Wadden Islands archipelago and the Wadden Sea. It was decided to use a controlled directional drilling as the only possible and least invasive method of cable installation in those conditions.

4

Asymptotics of the supremum of scaled Brownian motion

Dębicki K.

Probability and Mathematical Statistics

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2001

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Vol. 21, Fasc. 1

199--212

EN

We consider the problem of estimating the tail of the distribution of the supremum of scaled Brownian motion B(ƒ(t)) processes with linear drift.Using the local time technique we obtain asymptotics and bounds of Pt≥t0(sup(B(ƒ(t))−t)> u), which are expressed in terms of the expected value of thelocal timeof B(ƒ(t))−tprocesses at levelu.As an application we obtain upper bounds for the tail of distribution of the supremum for some Gaussian processes with stationary increments.