# Exact simulation of max-stable processes

arXiv: https://arxiv.org/abs/1506.04430 · HTML: https://mlsanity.com/paper/1506.04430/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2015.

## Built on by (most cited first, 6 of 6)

- [Modeling Extremes with d-max-decreasing Neural Networks](https://mlsanity.com/paper/2102.09042/) (2021)
- [Theoretical guarantees for neural estimators in parametric statistics](https://mlsanity.com/paper/2506.18508/) (2025)
- [Extremal graphical modeling with latent variables via convex optimization](https://mlsanity.com/paper/2403.09604/) (2024)
- [Distributionally Robust Optimization as a Scalable Framework to Characterize Extreme Value Distributions](https://mlsanity.com/paper/2408.00131/) (2024)
- [Adaptive generative moment matching networks for improved learning of dependence structures](https://mlsanity.com/paper/2508.21531/) (2025)
- [Multi-output Extreme Spatial Model for Complex Aircraft Production Systems](https://mlsanity.com/paper/2604.22548/) (2026)

## Abstract (arXiv)

Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes simulation highly nontrivial. Algorithms based on finite approximations that are used in practice are often not exact and computationally inefficient. We will present two algorithms for exact simulation of a max-stable process at a finite number of locations. The first algorithm generalizes the approach by citetDM-2014 for Brown--Resnick processes and it is based on simulation from the spectral measure. The second algorithm relies on the idea to simulate only the extremal functions, that is, those functions in the construction of a max-stable process that effectively contribute to the pointwise maximum. We study the complexity of both algorithms and prove that the second procedure is always more efficient. Moreover, we provide closed expressions for their implementation that cover the most popular models for max-stable processes and extreme value copulas. For simulation on dense grids, an adaptive design of the second algorithm is proposed.