Integrability of absolutely continuous transformations of measures and applications to optimal mass transportation

被引：2
|
作者：
Bogachev, V. I.
Kolesnikov, A. V.
机构：
[1] MSU, Lab Math Stat, Fac Mech & Math, Moscow 119992, Russia
[2] Scuola Normale Super Pisa, Ctr Ric Matemat Ennio De Giorgi, I-56100 Pisa, Italy
来源：
THEORY OF PROBABILITY AND ITS APPLICATIONS | 2006年 / 50卷 / 03期
关键词：
optimal transportation; Gaussian measure; convex measure; logarithmic Sobolev inequality; Poincare inequality; Talagrand inequality;
D O I：
10.1137/S0040585X97981810
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Given two Borel probability measures mu and nu on R-d such that d nu/d mu = g, we consider certain mappings of the form T( x) = x + F( x) that transform mu into nu. Our main results give estimates of the form integral(d)(R)Phi(1)(vertical bar F vertical bar)d mu <= integral(d)(R) Phi(2)(g)d mu for certain functions Phi(1) and Phi(2) under appropriate assumptions on mu. Applications are given to optimal mass transportations in the Monge problem.
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页码：367 / 385
页数：19
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