The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any...

We discuss three forms of convergence in distribution which are stronger than the normal weak convergence, and are non-topological in nature. We give Storokhod representation results for two of these modes of convergence, and give applications to sufficient statistics and conditioned Markov...

An embedding of an arbitrary centred law [mu] in a Brownian motion (that is a stopping time T and a Brownian motion B such that (Bt)=[mu] and (Bt[Lambda]T; t[greater-or-equal, slanted]0) is found such that B*T has a law which dominates that of M*[tau], where the pair (M, [tau]) is any other ui...