Simulationsverfahren fuer Brown-Resnick-Prozesse (Simulation Techniques for Brown-Resnick Processes)

TL;DR

This paper introduces new simulation methods for generalized Brown-Resnick processes, addressing the challenge of efficient and accurate finite approximations, especially for processes generated by dissipative flows.

Contribution

It presents alternative representations and finite approximation techniques for Brown-Resnick processes, including error bounds, improving simulation accuracy and efficiency.

Findings

New representations enable better finite approximations.

Error bounds for original processes are derived.

Simulation methods reduce approximation errors and computation time.

Abstract

Generalized Brown-Resnick processes form a flexible class of stationary max-stable processes based on Gaussian random fields. With regard to applications fast and accurate simulation of these processes is an important issue. In fact, Brown-Resnick processes that are generated by a dissipative flow do not allow for good finite approximations using the definition of the processes. On large intervals we get either huge approximation errors or very long operating times. Looking for solutions of this problem, we give different representations of the generalized Brown-Resnick processes - including random shifting and a mixed moving maxima representation - and derive various kinds of finite approximations that can be used for simulation purposes. Furthermore, error bounds are calculated in the case of the original process by Brown and Resnick (1977).