Abstract
By a classical result of [10] the ρ{variant} distance between stationary processes is identified with an optimal stationary coupling problem of the corresponding stationary measures on the infinite product spaces. This is a modification of the optimal coupling problem from Monge-Kantorovich theory. In this paper we derive some general classes of examples of optimal stationary couplings which allow to calculate the ρ{variant} distance in these cases in explicit form. We also extend the ρ{variant} distance to random fields and to general nonmetric distance functions and give a construction method for optimal stationary c-couplings. Our assumptions need in this case a geometric positive curvature condition.
Original language | English |
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Journal | Electronic Journal of Probability |
Volume | 17 |
DOIs | |
Publication status | Published - 2012 |
Keywords
- Monge-Kantorovich theory
- Optimal stationary couplings
- Stationary processes
- ρ{variant}-distance
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty