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Minimal Metrics in the Random Variables Space

In: Probability and Statistical Inference

Author

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  • Svetlozar T. Rachev

    (Institute of Mathematics Bulgarian Academy of Sciences)

Abstract

Let (U,d) be a separable metric space with metric d. Consider the space V=V(U,d) of all U-valued random variables X on certain probability space. For every probability metric μ(X,Y) on V we define the minimal probability metric $$\hat L$$ (X,Y)=inf (X,Y), where the infimum is taken over the set of all joint distributions JD(X,Y) with fixed marginals D(X) and D(Y). Let Lp(X,Y)=(Edp(X,Y))1/p for p≥1, and lp= $$\hat \mu $$ p. The aim of the paper is to carry out an analysis of the convergence in lp metric.

Suggested Citation

  • Svetlozar T. Rachev, 1982. "Minimal Metrics in the Random Variables Space," Springer Books, in: Wilfried Grossmann & Georg Ch. Pflug & Wolfgang Wertz (ed.), Probability and Statistical Inference, pages 319-327, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-7840-9_30
    DOI: 10.1007/978-94-009-7840-9_30
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