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From snapping out Brownian motions to Walsh's spider processes on star-like graphs
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abstract
By analyzing matrices involved, we prove that a snapping-out Brownian motion with large permeability coefficients is a good approximation of Walsh's spider process on the star-like graph $K_{1,k}$. Thus, the latter process can be seen as a Brownian motion perturbed by a trace of semi-permeable membrane at the graph's center.
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Cited by 1 Pith paper
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General diffusions on metric graphs as limits of time-space Markov Chains
A new space-time Markov chain approximation for general diffusions on metric graphs is shown to converge in p-Wasserstein distance at explicit rates governed by a thinness quantifier of the subdivision.
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