Coupling all the L\'evy 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 L\'evy stochastic areas ∫ Bi dBj-∫ Bj dBi. It is conjectured that successful co-adapted couplings still exist when the L\'evy stochastic areas are replaced by a finite set of multiply iterated path- and time-integrals, subject to algebraic compatibility of the initial conditions.
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