Non-Markovian maximal couplings and a vertical reflection principle on a
class of sub-Riemannian manifolds
Non-Markovian maximal couplings and a vertical reflection principle on a
class of sub-Riemannian manifolds
We develop non-Markovian, non-co-adapted couplings for sub-Riemannian Brownian motions in various sub-Riemannian manifolds, namely the three-dimensional Heisenberg group, higher-dimensional non-isotropic Heisenberg groups, SL(2,R) and its universal cover, and SU(2,C). Our primary focus is on the situation when the processes start from two points on the same vertical fiber, since in …