Optimal transport maps on infinite dimensional spaces

doi:10.1007/s11464-015-0474-y

Front. Math. China

2015, Vol. 10

Issue (4) : 715-732 https://doi.org/10.1007/s11464-015-0474-y

SURVEY ARTICLE

Optimal transport maps on infinite dimensional spaces

Shizan FANG(

),Vincent NOLOT

I.M.B., BP 47870, Université de Bourgogne, Dijon, France In memory of Denis Feyel

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Abstract

We will give a survey on results concerning Girsanov transformations, transportation cost inequalities, convexity of entropy, and optimal transport maps on some infinite dimensional spaces. Some open Problems will be arisen.

Keywords Girsanov theorem entropy optimal transport map Wiener space Lebesgue point

Corresponding Author(s): Shizan FANG

Issue Date: 05 June 2015

Cite this article:

Shizan FANG,Vincent NOLOT. Optimal transport maps on infinite dimensional spaces[J]. Front. Math. China, 2015, 10(4): 715-732.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0474-y
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I4/715

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