Coupling all the Lévy stochastic areas of multidimensional Brownian motion
Kendall, Wilfrid S.
Ann. Probab., Tome 35 (2007) no. 1, p. 935-953 / Harvested from Project Euclid
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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 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.
Publié le : 2007-05-14
Classification:  Brownian motion,  co-adapted coupling,  exotic coupling,  Lévy stochastic area,  nonco-adapted coupling,  stochastic differential,  60J65,  60H10 
@article{1178804319,
     author = {Kendall, Wilfrid S.},
     title = {Coupling all the L\'evy stochastic areas of multidimensional Brownian motion},
     journal = {Ann. Probab.},
     volume = {35},
     number = {1},
     year = {2007},
     pages = { 935-953},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1178804319}
}

Kendall, Wilfrid S. Coupling all the Lévy stochastic areas of multidimensional Brownian motion. Ann. Probab., Tome 35 (2007) no. 1, pp.  935-953. http://gdmltest.u-ga.fr/item/1178804319/