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 |
|---|---|
| Journal | Electronic Journal of Probability |
| Volume | 17 |
| DOIs | |
| Publication status | Published - 2012 |
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Keywords
- ρ{variant}-distance
- Monge-Kantorovich theory
- Optimal stationary couplings
- Stationary processes
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
Cite this
On optimal stationary couplings between stationary processes. / Rüschendorf, Ludger; Sei, Tomonari.
In: Electronic Journal of Probability, Vol. 17, 2012.Research output: Contribution to journal › Article
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TY - JOUR
T1 - On optimal stationary couplings between stationary processes
AU - Rüschendorf, Ludger
AU - Sei, Tomonari
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
KW - ρ{variant}-distance
KW - Monge-Kantorovich theory
KW - Optimal stationary couplings
KW - Stationary processes
UR - http://www.scopus.com/inward/record.url?scp=84859070177&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84859070177&partnerID=8YFLogxK
U2 - 10.1214/EJP.v17-1797
DO - 10.1214/EJP.v17-1797
M3 - Article
AN - SCOPUS:84859070177
VL - 17
JO - Electronic Journal of Probability
JF - Electronic Journal of Probability
SN - 1083-6489
ER -