Transfunctions applied to plans, Markov operators and optimal transport

Jason Bentley; Piotr Mikusiński

Published: 2024-10-29

2024

Transfunctions applied to plans, Markov operators and optimal transport

Jason Bentley

, Piotr Mikusiński

Abstract

A transfunction is a function which maps between sets of finite measures on measurable spaces. In this paper we characterize transfunctions that correspond to Markov operators and to plans; such a transfunction will contain the “instructions” common to several Markov operators and plans. We also define the adjoint of transfunctions in two settings and provide conditions for existence of adjoints. Finally, we develop approximations of identity in each setting and use them to approximate weakly-continuous transfunctions with simple transfunctions; one of these results can be applied to some optimal transport problems to approximate the optimal cost with simple Markov transfunctions.

Keywords:

Markov operator , plan , Radon adjoint , transfunction , transport

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Bentley, J., & Mikusiński, P. (2024). Transfunctions applied to plans, Markov operators and optimal transport. Annales Mathematicae Silesianae. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/18062

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2024
Published: 2024-01-18

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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