Coupling all the Lévy stochastic areas of multidimensional Brownian motion

Abstract

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 Lévy stochastic areas $\int B_{i}d{B}_j-\int B_{j}d{B}_i$. 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.

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

References in corpus (3)

• Exact simulation of diffusions
• Controlled diffusion processes
• Optimally coupling the Kolmogorov diffusion, and related optimal control problems

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