ON GENERALIZED MAX-LINEAR MODELS IN MAX-STABLE RANDOM FIELDS MICHAEL FALK, MAXIMILIAN ZOTT Abstract. In practice, it is not possible to observe a whole max-stable ran- dom field. Therefore, a way how to reconstruct a max-stable random field in C ( [0 , 1] $^{k}$) by interpolating its realizations at finitely many points is proposed. The resulting interpolating process is again a max-stable random field. This approach uses a generalized max-linear model. Promising results have been established in the case k = 1 in a previous paper. However, the extension to higher dimensions is not straightforward since we lose the natural order of the index space. Dombry et al. (2013) derive an algorithm to sample from the regular conditional distribution of a max-stable random field η , say, given the marginal observations η$_{s}$$_{1}$ = z$_{1}$, . . . , η$_{s}$$_{k}$ = z$_{k}$ for some z$_{1}$, . . . , z$_{d}$ from the state space and k locations s$_{1}$, . . . , s$_{d}$ . This, clearly, concerns the distribution of η and derived distributional parameters. Different to that, we try to reconstruct η from the observations η$_{s}$$_{1}$ , . . . , η$_{s}$$_{k}$ . This is done by a generalized max-linear model in such a way, that the interpolating process ˆ η is again a (standard) max-stable random field. As our approach is deterministic, once the observations η$_{s}$$_{1}$ = z$_{1}$, . . . , η$_{s}$$_{k}$ = z$_{k}$ are given, a proper way to measure the performance of our approach is the mean squared error (MSE). Convergence of the pointwise MSE as well as of the integrated 1. Introduction and Preliminaries arXiv:1703.03472v1 [math.PR] 9 Mar 2017 2010 Mathematics Subject Classification. Primary 60G70. Key words and phrases. Multivariate extreme value distribution • max-stable random field • D -norm • max-linear model • stochastic interpolation. 1