English

Shift-generated $\alpha$-homogeneous classes of jointly measurable random fields

Probability 2025-07-28 v1 Methodology

Abstract

We consider a class of shift-generated alpha-homogeneous random fields (RFs) C[Z] defined through a functional identity involving a fixed positive alpha and a given jointly measurable R^d-valued RF Z(t),t in R^l. The significance of such classes lies in the fact that their elements generate max-stable and stationary RFs. We extend the original functional identity to a broad class of functionals, including the integral operator S(.) and prove that C[Z] contains at least one L^alpha-continuous element. Finally, we investigate properties of local RFs and their connections with spectral tail and tail RFs.

Cite

@article{arxiv.2507.18835,
  title  = {Shift-generated $\alpha$-homogeneous classes of jointly measurable random fields},
  author = {Enkelejd Hashorva},
  journal= {arXiv preprint arXiv:2507.18835},
  year   = {2025}
}
R2 v1 2026-07-01T04:17:58.207Z