Coupling all the Lévy stochastic areas of multidimensional Brownian motion

Details Coupling all the Lévy stochastic areas of multidimensional Brownian motion Coupling all the Lévy stochastic areas of multidimensional Brownian motion

2005-12-14

arxiv.org/abs/math/0512336v2

Annals of Probability 2007, Vol. 35, No. 3, 935-953

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000001196 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000001196

It is shown how to construct a successful co-adapted coupling of two copies of an $n$-dimensional Brownian motion $(B_1,...,B_n)$ while simultaneously coupling all corresponding copies of L\'{e}vy stochastic areas $\int B_i dB_j-\int B_j dB_i$. It is conjectured that successful co-adapted couplings still exist when the L\'{e}vy 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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