Diffusion processes on graphs: stochastic differential equations, large deviation principle

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Brownian motions on metric graphs (2011, background): “5) at the vertices? Can one say something about large deviations as done for example for Brownian motions without killing and more generally for conservative diffusion processes in [30]? What form does the Itô formula take in the case of a diffusion process on a metric graph with a generator subject”
Corrections for "Occupation and local times for skew Brownian motion with applications to dispersion across an interface" (2010, background): “A determination of the (joint) distributions of key functionals of standard skew Brownian motion together with some associated probabilistic semigroup and local time theory is given for these purposes.”