  The evolution by horizontal mean curvature flow (HMCF) is a partial
differential equation in a sub-Riemannian setting with application in IT and
neurogeometry (see Citti-Franceschiello-Sanguinetti-Sarti, 2016). Unfortunately
this equation is difficult to study, since the horizontal normal is not always
well defined. To overcome this problem the Riemannian approximation was
introduced. In this article we define a stochastic representation of the
solution of the approximated Riemannian mean curvature using the Riemannian
approximation and we will prove that it is a solution in the viscosity sense of
the approximated mean curvature flow, generalizing the result of
Dirr-Dragoni-von Renesse, 2010.
