For spider diffusions with a local-time dependent spinning measure, the paper proves Itô calculus, no atom at the junction, Feynman-Kac representations, local-time approximations, the strong Markov property, and vertex scattering limits.
Embedding of Walsh Brownian mo tion, Stochastic Processes and their Applications; 134, p.1-28, 2021
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On spider diffusions having a spinning measure selected from their own local time
For spider diffusions with a local-time dependent spinning measure, the paper proves Itô calculus, no atom at the junction, Feynman-Kac representations, local-time approximations, the strong Markov property, and vertex scattering limits.