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Найдено 5 публикаций
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Статья
Kolesnikov A., Zaev D. Theory of Stochastic Processes. 2015. Vol. 20(36). No. 2. P. 54-62.

We study the Monge and Kantorovich transportation problems on R∞R∞ within the class of exchangeable measures. With the help of the de Finetti decomposition theorem the problem is reduced to an unconstrained optimal transportation problem on a Hilbert space. We find sufficient conditions for convergence of finite-dimensional approximations to the Monge solution. The result holds, in particular, under certain analytical assumptions involving log-concavity of the target measure. As a by-product we obtain the following result: any uniformly log-concave exchangeable sequence of random variables is i.i.d. 

 

 

Добавлено: 8 июля 2016
Статья
Kolesnikov A., Kosov E. Theory of Stochastic Processes. 2017. Vol. 22. No. 38. P. 47-61.
Добавлено: 21 августа 2018
Статья
Veretennikov A. Theory of Stochastic Processes. 2017. No. 1. P. 88-102.
Добавлено: 17 октября 2017
Статья
Bogachev V., Miftakhov A. Theory of Stochastic Processes. 2016. Vol. 21(37). No. 1. P. 1-11.

We study conditions on metrics on spaces of measurable functions under which weak convergence of Borel probability measures on these spaces follows from weak convergence of finite-dimensional projections of the considered measures. 

Добавлено: 14 декабря 2016
Статья
Kolesnikov A., Lysenko N. Y. Theory of Stochastic Processes. 2016. Vol. 21(37). No. 2. P. 22-28.

We study the Monge--Kantorovich problem with one-dimensional marginals $\mu$ and $\nu$ and

the cost function $c = \min\{l_1, \ldots, l_n\}$

that equals the minimum of a finite number $n$ of affine functions $l_i$

satisfying certain non-degeneracy assumptions. We prove that the problem

is equivalent to a finite-dimensional extremal problem. More precisely, it is shown that the solution is concentrated

on the union of $n$ products $I_i \times J_i$, where $\{I_i\}$ and $\{J_i\}$

are partitions of the real line into unions of disjoint connected sets.

The families of sets $\{I_i\}$ and $\{J_i\}$ have the following properties: 1) $c=l_i$ on $I_i \times J_i$,

2) $\{I_i\}, \{J_i\}$ is a couple of partitions solving an auxiliary $n$-dimensional extremal problem.

The result is partially generalized to the case of more than two marginals.

Добавлено: 30 декабря 2017