The intersections of images of trajectories for independent Brownian motions on Carnot groups

Oleksii Rudenko
Theory of Stochastic Processes
Vol.30 (46), no.1, 2026, pp.61-84

In this paper we present the conditions for the existence of intersections for functions of several independent Brownian motions on Carnot groups. These conditions are geometrical and local in nature, in the sense that they give a simple relation between the local geometry of a manifold, related to intersections, at a given point, with the structure of Lie algebra of left-invariant vector fields in a neighbourhood of the same point. We prove that these conditions are necessary and sufficient for the existence of intersections, if we exlcude from the consideration the points of a nowhere dense set on the manifold, related to intersections.

DOI: https://doi.org/10.3842/tsp-0860773337-95
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