2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77872A stochastic flow is constructed on a frame bundle adapted to a Riemannian foliation on a compact manifold. The generator A of the resulting transition semigroup is shown to preserve the basic functions and forms, and there is an essentially unique strictly positive smooth function phi satisfying A^* phi = 0. This function is used to perturb the metric, and an application of the ergodic theorem shows that there exists a bundle-like metric for which the basic projection of the mean curvature is basic-harmonic.LaTex, 36 pages, no figures. To appear in Houston Journal of MathematicsDifferential GeometryProbabilitytext