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.
Walsh Spider Diffusions as Time Changed Multi-parameter Processes
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abstract
Inspired by allocation strategies in multi-armed bandit model, we propose a pathwise construction of Walsh spider diffusions. For any infinitesimal generator on a star shaped graph, there exists a unique time change associated with a multi-parameter process such that the time change of this multi-parameter process is the desired diffusion. The time change has an interpretation of time allocation of the process on each edge, and it can be derived explicitly from a family of equations.
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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.