71 citations · 163 across the 16 of their papers we have counts for
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Construction of the Paths of Brownian Motions on Star Graphs
Vadim Kostrykin, Jürgen Potthoff, Robert Schrader
Pathwise constructions of Brownian motions which satisfy all possible boundary conditions at the vertex of star graphs are given.
A Note on Feller Semigroups and Resolvents
Vadim Kostrykin, Jürgen Potthoff, Robert Schrader
Various equivalent conditions for a semigroup or a resolvent generated by a Markov process to be of Feller type are given.
Brownian Motions on Metric Graphs III - Construction: General Metric Graphs
Vadim Kostrykin, Jürgen Potthoff, Robert Schrader
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 Bro…
Brownian Motions on Metric Graphs II - Construction of Brownian Motions on Single Vertex Graphs
Vadim Kostrykin, Jürgen Potthoff, Robert Schrader
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
Vadim Kostrykin, Jürgen Potthoff, Robert Schrader
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…