A1223
Title: Extending Brown-Resnick stationarity to the max-domain of attraction
Authors: Ioan Scheffel - University of Stuttgart (Germany) [presenting]
Abstract: We develop a new framework for constructing stationary max-infinitely divisible (max-id) processes using stochastic differential equations (SDEs). Inspired by the Brown-Resnick process, we consider particle systems driven by Markovian dynamics and initialized by a Poisson point process. Given a target marginal distribution, we construct a diffusion process whose invariant measure matches the Poisson intensity, thereby ensuring stationarity of the resulting max-id process. We establish well-posedness of the SDE, characterize the invariant structure, and prove convergence to a Brown-Resnick-type process under rescaling. This approach extends classical max-stable constructions to a broader class of max-id models, enabling more flexible dependence structures.
