Asymptotic analysis of the optimal cost in some transportation problems with random locations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:122

Article

Torrisi, Giovanni Luca

关键词: Calculus of variations;    Central limit theorem;    Large deviations;    Matching problem;    Moderate deviations;    Monge-Kantorovich problem;    Optimal transport;   

DOI  :  10.1016/j.spa.2011.08.009

来源: Elsevier

【 摘 要 】

In this paper we provide an asymptotic analysis of the optimal transport cost in some matching problems with random locations. More precisely, under various assumptions on the distribution of the locations and the cost function, we prove almost sure convergence, and large and moderate deviation principles. In general, the rate functions are given in terms of infinite-dimensional variational problems. For a suitable one-dimensional transportation problem, we provide the expression of the large deviation rate function in terms of a one-dimensional optimization problem, which allows the numerical estimation of the rate function. Finally, for certain one-dimensional transportation problems, we prove a central limit theorem. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free