Non co-adapted couplings of Brownian motions on free, step 2 Carnot groups

2024/07/09 by Bénéfice, Magalie
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2407.06593

Abstract

On the free, step 2 Carnot groups of rank n \mathbbG_n, the subRiemannian Brownian motion consists in a ℝⁿ-Brownian motion together with its (n(n-1))/(2) Lévy areas. In this article we construct an explicit successful non co-adapted coupling of Brownian motions on \mathbbG_n. We use this construction to obtain gradient inequalities for the heat semi-group on all the homogeneous step 2 Carnot groups. Comparing the first coupling time and the first exit time from a domain, we also obtain gradient inequalities for harmonic functions on \mathbbG_n. These results generalize the coupling strategy by Banerjee, Gordina and Mariano on the Heisenberg group.

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