Kostrykin, Vadim; Potthoff, Jürgen; Schrader, Robert
Year of publication:
Brownian motions on a metric graph are defined. Their generators are
characterized as Laplace operators subject to Wentzell boundary at every
vertex. Conversely, given a set of Wentzell boundary conditions at the
vertices of a metric graph, a Brownian motion is constructed pathwise on this
graph so that its generator satisfies the given boundary conditions.