Preserving the multivariate tail measure is necessary and sufficient for a generator to recover first-order rare joint-stress probabilities and scaled conditional laws; SSGEN implements this via Pareto radial extrapolation plus a learned angular law.
Further, since the feasible set Γu(J) is contained in{∥z∥>c}, the solution sets are contained in BM∩B cc, wherecis as defined in Lemma 11, for all sufficiently largeu
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Simulating Stress Laws under Extremal Dependence: Characterizing What Generative Models Must Preserve
Preserving the multivariate tail measure is necessary and sufficient for a generator to recover first-order rare joint-stress probabilities and scaled conditional laws; SSGEN implements this via Pareto radial extrapolation plus a learned angular law.