Couplings of Brownian motions on SU(2) and SL(2,R)

Magalie Bénéfice

Stochastic Processes and their Applications, 2024, vol. 176, issue C

Abstract: The Lie groups SU(2) and SL(2,R) can be viewed as model spaces in subRiemannian geometry. Coupling two subelliptic Brownian motions on SU(2) (resp. SL(2,R)) consists in simultaneously coupling two Brownian motions on the sphere (resp. the hyperbolic plane) and their swept areas. Using this approach we propose an explicit construction of a co-adapted successful coupling on SU(2). The strategy is to alternate between reflection and synchronous (with noise) couplings on the sphere. We also describe some more general constructions of co-adapted couplings on SU(2) and on SL(2,R).

Keywords: SubRiemannian manifolds; Brownian motion; Coupling; Co-adapted coupling; Successful coupling (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104434

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