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Operations Research Seminar - "About ratios of homogeneous functionals acting on a heavy-tailed time series ” - Thomas Mikosch, University of Copenhagen

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We consider a real-valued regularly varying stationary sequence with infinite variance and construct homogeneous functionals from a sample of this sequence. These include the maximum of the sample, its sum, lp norms, and their powers. First, we prove the joint convergence of these quantities via transform arguments (hybrid characteristic functions, Laplace transforms). This implies the convergence of their ratios, and we also provide characterizations of their limit ratio and calculation of their moments.
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