Consider an asymptotic two-sample test for the hypothesis that two stationary random fields have the same mean functionals. The asymptotics here is understood in the sense of an observation window expanding to the whole Euclidean space. Provided that only one realization of the fields is available the goal is to use asymptotic as well as randomization techniques to make this test valid. In the latter case "valid" means finitely exact for a compact observation window. Here, an overview of randomization approaches from the literature has to be given as well. The thesis should conclude with a numerical simulation study showing the performance of the tests.

This thesis will be supervised jointly by the Institutes of Statistics and Stochastics.

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