Natalia Soja-Kukieła

activity

20132020

collaborators

5 papers

math.PR2020

Directional phantom distribution functions for~stationary random fields

Adam Jakubowski, Igor Rodionov, Natalia Soja-Kukieła

We give necessary and sufficient conditions for the existence of a phantom distribution function for a stationary random field on a regular lattice. We also introduce a less demand…

math.PR2018

On maxima of stationary fields

Natalia Soja-Kukieła

Let ${X_{n} : n \in Z^{d}}$ be a weakly dependent stationary field with maxima $M_{A} := sup {X_{i} : i \in A}$ for finite $A\subset\mat…

math.PR2017

Asymptotics of the order statistics for a process with a regenerative structure

Natalia Soja-Kukieła

In the paper, a regenerative process ${X_{n} : n \in N}$ with finite mean cycle length is considered. For~ $M_{n}^{(q)}$ denoting the $q$ -th largest value in $\{X_k : 1\leqslant…

math.PR2016

Extremes of multidimensional stationary Gaussian random fields

Natalia Soja-Kukieła

Let ${X (t) : t = (t_{1}, t_{2}, \dots, t_{d}) \in [0, \infty)^{d}}$ be a centered stationary Gaussian field with almost surely continuous sample paths, unit variance and corr…

math.PR2013

Extremes of homogeneous Gaussian random fields

Krzysztof Dębicki, Enkelejd Hashorva, Natalia Soja-Kukieła

Let ${X (s, t) : s, t ⩾ 0}$ be a centered homogeneous Gaussian field with a.s. continuous sample paths and correlation function $r (s, t) = C o v (X (s, t), X (0, 0))$ such that \[r(s,t)=1…