Extremum problems with total variation distance
Extremum problems with total variation distance
The aim of this paper is to investigate extremum problems with pay-off the total variational distance metric subject to linear functional constraints both defined on the space of probability measures, as well as related problems. Utilizing concepts from signed measures, the extremum probability measures of such problems are obtained in closed form, by identifying the partition of the support set and the mass of these extremum measures on the partition. The results are derived for abstract spaces, specifically, complete separable metric spaces, while the high level ideas are also discussed for denumerable spaces endowed with the discrete topology.
- Royal Institute of Technology Sweden
- University of Ottawa Canada
- University of Cyprus Cyprus
Total variation, Discrete topology, Control, Abstract space, Linear functional, Probability measures, Variational distance, Topology, Signed measure, Separable metric spaces
Total variation, Discrete topology, Control, Abstract space, Linear functional, Probability measures, Variational distance, Topology, Signed measure, Separable metric spaces
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