Vadim Kostrykin, Jürgen Potthoff, Robert Schrader
Published 2011-02-24, updated 2012-05-01Version 3
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.
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
Brownian Motions on Metric Graphs III - Construction: General Metric Graphs
On Besov regularity of Brownian motions in infinite dimensions
Chernoff's Theorem and Discrete Time Approximations of Brownian Motion on Manifolds
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