# On generalized max-linear models in max-stable random fields

## TL;DR

This paper proposes a method to reconstruct max-stable random fields in multi-dimensional spaces using generalized max-linear models, extending previous one-dimensional results to higher dimensions despite the loss of natural order.

## Contribution

It introduces a novel approach for interpolating max-stable fields in higher dimensions, generalizing existing methods from one-dimensional cases.

## Key findings

- Successful extension of max-linear models to higher dimensions
- Interpolation preserves max-stability in reconstructed fields
- Promising results in one-dimensional case suggest potential for multi-dimensional applications

## Abstract

In practice, it is not possible to observe a whole max-stable random field. Therefore, a way how to reconstruct a max-stable random field in $C\left([0,1]^k\right)$ by interpolating its realizations at finitely many points is proposed. The resulting interpolating process is again a max-stable random field. This approach uses a \emph{generalized max-linear model}. Promising results have been established in the case $k=1$ in a previous paper. However, the extension to higher dimensions is not straightforward since we lose the natural order of the index space.