On optimal stationary couplings between stationary processes
نویسندگان
چکیده
By a classical result of Gray et al. (1975) the %̄ 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 %̄ distance in these cases in explicit form. We also extend the %̄ distance to random fields and to general nonmetric distance functions and give a construction method for optimal stationary c̄-couplings. Our assumptions need in this case a geometric positive curvature condition.
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