2018/05/28 by Werner, Florian
#05C99 #35K05 #58J65 #60H99 #60J45 #60J65 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1805.10905
A pathwise construction of discontinuous Brownian motions on metric graphs is given for every possible set of non-local Feller-Wentzell boundary conditions. This construction is achieved by locally decomposing the metric graphs into star graphs, establishing local solutions on these partial graphs, pasting the solutions together, introducing non-local jumps, and verifying the generator of the resulting process.