Open Access
May 2007 Coupling all the Lévy stochastic areas of multidimensional Brownian motion
Wilfrid S. Kendall
Ann. Probab. 35(3): 935-953 (May 2007). DOI: 10.1214/009117906000001196


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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Wilfrid S. Kendall. "Coupling all the Lévy stochastic areas of multidimensional Brownian motion." Ann. Probab. 35 (3) 935 - 953, May 2007.


Published: May 2007
First available in Project Euclid: 10 May 2007

zbMATH: 1133.60033
MathSciNet: MR2319712
Digital Object Identifier: 10.1214/009117906000001196

Primary: 60H10 , 60J65

Keywords: Brownian motion , Co-adapted coupling , exotic coupling , Lévy stochastic area , nonco-adapted coupling , stochastic differential

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 3 • May 2007
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