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Brownian Motions on Metric Graphs III - Construction: General Metric Graphs
Brownian motion metric graph Wentzell boundary condition
2011/1/18
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 s...
Brownian Motions on Metric Graphs II - Construction of Brownian Motions on Single Vertex Graphs
Brownian motion Feller Brownian motion metric graphs
2011/1/18
Pathwise constructions of Brownian motions which satisfy all possible boundary conditions at the vertex of single vertex graphs are given.
Brownian Motions on Metric Graphs I - Definition, Feller Property, and Generators
Metric graphs Brownian motion Feller processes Feller’s theorem
2011/1/18
Brownian motions on a metric graph are defined, their Feller property is proved, and their generators are characterized. This yields a version of Feller’s theorem for metric graphs.