Brownian motion in Riemannian admissible complexes (Q2567518)

The purpose of the work is to construct a Brownian motion on a simplicial complex with a piecewise differential structure. The author constructs there, first, so called isotropic transport processes and then shows that there are weakly converging subsequences of these processes whose limits he calls Brownian motions. Finally, the author gives a sufficient condition for transience of such a Brownian motion on a 2-dimensional noncompact simply connected Riemannian complex with nonpositive curvature.