It is shown how to construct a successful co-adapted coupling of two copies of an n-dimensional Brownian motion (B1,...,Bn) while simultaneously coupling all corresponding copies of Lévy stochastic areas � Bi dBj − � Bj dBi. It is conjectured that successful coadapted couplings still exist when the Lévy stochastic areas are replaced by a finite set of multiply iterated path- and time-integrals, subject to algebraic compatibility of the initial conditions. 1. Introduction.
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