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Walsh Spider Diffusions as Time Changed Multi-parameter Processes
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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.
Forward citations
Cited by 2 Pith papers
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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 verte...
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Stochastic scattering control of spider diffusion governed by an optimal diffraction probability measure selected from its own local-time
For a spider diffusion with controlled, local-time-dependent branch selection, the value function is characterized as the unique viscosity solution of a HJB system with a nonlinear local-time Kirchhoff boundary condition.
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