Coupling all the lévy stochastic areas of multidimensional brownian motion

Abstract

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 d Bj - ∫ Bj d Bi. It is conjectured that successful co-adapted 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. © Institute of Mathematical Statistics, 2007.