6533b82efe1ef96bd1293cda

RESEARCH PRODUCT

Optimal transport on the classical Wiener space with different norms

Vincent Nolot

subject

Mathematics - Functional AnalysisProbability (math.PR)FOS: MathematicsMathematics - ProbabilityFunctional Analysis (math.FA)

description

In this paper we study two basic facts of optimal transportation on Wiener space W. Our first aim is to answer to the Monge Problem on the Wiener space endowed with the Sobolev type norm (k,gamma) to the power of p (cases p = 1 and p > 1 are considered apart). The second one is to prove 1-convexity (resp. C-convexity) along (constant speed) geodesics of relative entropy in (P2(W);W2), where W is endowed with the infinite norm (resp. with (k,gamma) norm), and W2 is the 2-distance of Wasserstein.

yearjournalcountryeditionlanguage
2011-11-08
https://dx.doi.org/10.48550/arxiv.1111.1938