Brownian Motions on Metric Graphs
Probability
2015-05-27 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1102.4937,
title = {Brownian Motions on Metric Graphs},
author = {Vadim Kostrykin and Jürgen Potthoff and Robert Schrader},
journal= {arXiv preprint arXiv:1102.4937},
year = {2015}
}
Comments
43 pages, 7 figures. 2nd revision of our article 1102.4937: The introduction has been modified, several references were added. This article will appear in the special issue of Journal of Mathematical Physics celebrating Elliott Lieb's 80th birthday