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- W4288804566 abstract "We introduce and study a notion of strong duality for two classes of optimization problems commonly occurring in probability theory. That is, on an abstract measurable space $(Omega,mathcal{F})$, we say that an equivalence relation $E$ on $Omega$ satisfies ``strong duality'' if $E$ is $(mathcal{F}otimesmathcal{F})$-measurable and if there exists a sub-$sigma$-algebra $mathcal{G}$ of $mathcal{F}$ such that for all probability measures $mathbb{P},mathbb{P}'$ on $(Omega,mathcal{F})$ we have [ sup_{Ainmathcal{G}}vert mathbb{P}(A)-mathbb{P}'(A)vert = min_{tilde{mathbb{P}}inGamma(mathbb{P},mathbb{P}')}(1-tilde{mathbb{P}}(E)), ] where $Gamma(mathbb{P},mathbb{P}')$ denotes the space of couplings of $mathbb{P}$ and $mathbb{P}'$, and where ``min'' asserts that the infimum is in fact achieved. The results herein, which can be seen as a surprising extension of Kantorovich duality to a class of irregular costs, give wide sufficient conditions for strong duality to hold. These conditions allow us to recover many classical results and to prove novel results in stochastic calculus, random sequence simulation, and point process theory." @default.
- W4288804566 created "2022-07-30" @default.
- W4288804566 creator A5071805275 @default.
- W4288804566 date "2022-07-28" @default.
- W4288804566 modified "2023-09-24" @default.
- W4288804566 title "A Strong Duality Principle for Equivalence Couplings and Total Variation" @default.
- W4288804566 doi "https://doi.org/10.48550/arxiv.2207.14239" @default.
- W4288804566 hasPublicationYear "2022" @default.
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