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

TL;DR

This paper introduces an exact, unbiased simulation algorithm for continuous max-id processes, simplifying the process by avoiding complex conditional distributions and focusing on finite Poisson random measures, with applications to exchangeable sequences.

Contribution

It develops a novel algorithm for unbiased simulation of continuous max-id processes that relies solely on finite Poisson measures, improving efficiency and applicability.

Findings

Algorithm achieves unbiased simulation of max-id processes.

Efficient simulation of exchangeable max-id sequences demonstrated.

Framework applicable to max-stable and exogenous shock models.

Abstract

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.