Independence with Respect to Upper and Lower Conditional Probabilities Assigned by Hausdorff Outer and Inner Measures

Stochastic independence with respect to upper and lower conditional probabilities deined by Hausdorff outer and inner measures

A new model of coherent upper conditional prevision is proposed in a metric space. It is defined by the Choquet integral with respect to the s-dimensional Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its dimension s. Otherwise if the conditioning event has Hausdorff outer measure in its dimension equal to zero or infinity it is defined by ...

Stochastic independence with respect to upper and lower conditional probabilities defined by Hausdorff outer and inner measures

Coherence and Fuzzy Reasoning

Upper and lower conditional previsions are defined by the Choquet integral with respect to the Hausdorff outer and inner measures when the conditioning events have positive and finite Hausdorff outer or inner measures in their dimension; otherwise, when conditioning events have infinite or zero Hausdorff outer or inner measures in their dimension, they are defined by a 0-1 valued finitely, but ...

Coherent Upper Conditional Previsions Defined by Hausdorff Outer Measures to Forecast in Chaotic Dynamical Systems

Coherent conditional previsions and probabilities are tools to model and quantify uncertainties; they have been investigated in de Finetti [3], [4], Dubins [10] Regazzini [13], [14] and Williams [20]. Separately coherent upper and lower conditional previsions have been introduced in Walley [18], [19] and models of upper and lower conditional previsions have been analysed in Vicig et al. [17] an...

Characterization of a coherent upper conditional prevision as the Choquet integral with respect to its associated Hausdorff outer measure

A model of coherent upper conditional prevision for bounded random variables is proposed in a metric space. It is defined by the Choquet integral with respect to Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension. Otherwise, when the conditioning event has Hausdorff outer measure equal to zero or infinity in its Hausdorff...