Brownian Motions on Metric Graphs III - Construction: General Metric Graphs

Details Brownian Motions on Metric Graphs III - Construction: General Metric Graphs Brownian Motions on Metric Graphs III - Construction: General Metric Graphs

2010-12-03

arxiv.org/abs/1012.0739v2

Mathematics

Probability

version 02: references updated

Scientific paper

Consider a metric graph G with set of vertices V. Assume that for every vertex in V one is given a Wentzell boundary condition. It is shown how one can construct the paths of a Brownian motion on G such that its generator - viewed as an operator on the space of continuous functions vanishing at infinity - has a domain consisting of twice continuously differentiable functions satisfying these boundary conditions.

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