# Exact simulation of continuous max-id processes with applications to exchangeable max-id sequences

arXiv: https://arxiv.org/abs/2107.04630 · HTML: https://mlsanity.com/paper/2107.04630/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2021.

## Built on by (most cited first, 1 of 1)

- [Generative neural networks for characteristic functions](https://mlsanity.com/paper/2401.04778/) (2024)

## Abstract (arXiv)

An algorithm for the unbiased simulation of continuous max-(resp. min-)id stochastic processes is developed. The algorithm only requires the simulation of finite Poisson random measures on the space of continuous functions and avoids the necessity of computing conditional distributions of infinite (exponent)measures. The complexity of the algorithm is characterized in terms of the expected number of simulated atoms of the Poisson random measures on the space of continuous functions. Special emphasis is put on the simulation of exchangeable max-(or min-)id sequences, in particular exchangeable Sato-frailty sequences. Additionally, exact simulation schemes of exchangeable exogenous shock models and exchangeable max-stable sequences are sketched.