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

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arxiv 1012.0739 v2 pith:4R44OVBR submitted 2010-12-03 math.PR

Vadim Kostrykin , Jürgen Potthoff , Robert Schrader This is my paper · ORCID
classification math.PR
keywords metricboundarybrownianfunctionsgraphsassumeconditionconditions
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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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