Coupling all the Lévy stochastic areas of multidimensional Brownian motion
Wilfrid S. Kendall
Source: Ann. Probab. Volume 35, Number 3 (2007), 935-953.
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 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.
Primary Subjects: 60J65, 60H10
Keywords: Brownian motion; co-adapted coupling; exotic coupling; Lévy stochastic area; nonco-adapted coupling; stochastic differential
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1178804319
Digital Object Identifier: doi:10.1214/009117906000001196
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