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A metric space is a set M together with a real-valued function d(x, y)defined for x, y ∈ M that satisfies the following three conditions. First,d(x, y) ≥ 0 for every x, y ∈ M, and d(x, y) = 0 if and o...
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.