Couplings of Brownian Motions of deterministic distance in model spaces of constant curvature

Abstract

We consider the model space of constant curvature in dimension n and characterize all co-adapted couplings of Brownian motions on this space for which the distance between the processes is deterministic. In addition, the construction of the coupling is explicit for every choice of $ρ$ satisfying the above hypotheses.

This is an updated version which include the coupling construction on all model spaces of constant curvature