The Annals of Probability

Coupling all the Lévy stochastic areas of multidimensional Brownian motion

Wilfrid S. Kendall

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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 ∫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.

Article information

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

Dates
First available in Project Euclid: 10 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1178804319

Digital Object Identifier
doi:10.1214/009117906000001196

Mathematical Reviews number (MathSciNet)
MR2319712

Zentralblatt MATH identifier
1133.60033

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

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

Citation

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. https://projecteuclid.org/euclid.aop/1178804319


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