# On the continuity of Pickands constants

@article{Dbicki2022OnTC, title={On the continuity of Pickands constants}, author={Krzysztof Dȩbicki and Enkelejd Hashorva and Zbigniew Michna}, journal={Journal of Applied Probability}, year={2022}, volume={59}, pages={187 - 201} }

Abstract For a non-negative separable random field Z(t),
$t\in \mathbb{R}^d$
, satisfying some mild assumptions, we show that
$ H_Z^\delta =\lim_{{T} \to \infty} ({1}/{T^d}) \mathbb{E}\{{\sup_{ t\in [0,T]^d \cap \delta \mathbb{Z}^d } Z(t) }\} <\infty$
for
$\delta \ge 0$
, where
$0 \mathbb{Z}^d\,:\!=\,\mathbb{R}^d$
, and prove that
$H_Z^0$
can be approximated by
$H_Z^\delta$
if
$\delta$
tends to 0. These results extend the classical findings for Pickands constants
$H_{Z}^\delta…

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