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September 5, 2025Documenta MathematicaOpen Access

From snapping-out Brownian motions to Walsh’s spider processes on star-like graphs

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Convergence of a snapping-out Brownian motion approximates Walsh's spider process on star-like graphs.
Approximations involve large permeability coefficients and trace perturbations in a central semi-permeable membrane.
Utilizing the Lord Kelvin method, we analyze ergodic properties and convergence of cosine families associated with semigroups.
This work enhances understanding of approximation theorems and deepens insights into underlying graph structures.

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This analysis reveals convergence in Brownian motion via spider processes on star-like graphs, suggesting insights into permeability effects.

Bobrowski et al. (2025) studied this question.

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This analysis reveals convergence in Brownian motion via spider processes on star-like graphs, suggesting insights into permeability effects.