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

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  • Bénéfice, Magalie

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).

Suggested Citation

  • Bénéfice, Magalie, 2024. "Couplings of Brownian motions on SU(2) and SL(2,R)," Stochastic Processes and their Applications, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:spapps:v:176:y:2024:i:c:s0304414924001406
    DOI: 10.1016/j.spa.2024.104434
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