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From snapping out Brownian motions to Walsh's spider processes on star-like graphs (2406.16800v1)

Published 24 Jun 2024 in math.PR

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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