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We prove in this paper that the weighted volume of the set of integral transportation matrices between two integral histograms r and c of equal sum is a positive definite kernel of r and c when the se...
Transportation inequalities: From Poisson to Gibbs measures
Gibbs measures Poisson point processes transportation inequalities
2011/3/21
We establish an optimal transportation inequality for the Poisson measure on the configuration space. Furthermore, under the Dobrushin uniqueness condition, we obtain a sharp transportation inequality...
Transportation Approach to Some Concentration Inequalities in Product Spaces
Concentration Inequalities Product Spaces Transportation
2009/5/12
Let P be any product (Borel) probability measure on product (Polish) space E and for vectors x,y,z in E let f(x,y,z) be the number of coordinates k for which x_k neither equals y_k nor z_k. Using a tr...
Optimal Control for Absolutely Continuous Stochastic Processes and the Mass Transportation Problem
Absolutely continuous stochastic process mass transportation problem Salisburyfi problem
2009/4/29
We study the optimal control problem for Rd-valued absolutely continuous stochastic processes with given marginal distributions at every time. When $d=1$, we show the existence and the uniqueness of a...
Integral criteria for transportation cost inequalities
Transportation-cost inequalities OrliczSpaces
2009/4/22
In this paper, we provide a characterization of a large class of transportation-cost inequalities in terms of exponential integrability of the cost function under the reference probability measure. Ou...