The Annals of Probability

Coupling all the Lévy stochastic areas of multidimensional Brownian motion

Wilfrid S. Kendall

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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 ∫BidBj∫BjdBi. 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.

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Ann. Probab., Volume 35, Number 3 (2007), 935-953.

First available in Project Euclid: 10 May 2007

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Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65] 60H10: Stochastic ordinary differential equations [See also 34F05]

Brownian motion co-adapted coupling exotic coupling Lévy stochastic area nonco-adapted coupling stochastic differential


Kendall, Wilfrid S. Coupling all the Lévy stochastic areas of multidimensional Brownian motion. Ann. Probab. 35 (2007), no. 3, 935--953. doi:10.1214/009117906000001196.

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