Stochastic Monge-Kantorovich Problem and its Duality

Details Stochastic Monge-Kantorovich Problem and its Duality Stochastic Monge-Kantorovich Problem and its Duality

2009-12-31

arxiv.org/abs/1001.0094v3

Mathematics

Probability

12pages

Scientific paper

In this article we prove the existence of a stochastic optimal transference
plan for a stochastic Monge-Kantorovich problem by measurable selection
theorem. A stochastic version of Kantorovich duality and the characterization
of stochastic optimal transference plan are also established. Moreover,
Wasserstein distance between two probability kernels are discussed too.

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