Walsh spider diffusions as time changed multi-parameter processes

Erhan Bayraktar, Jingjie Zhang and Xin Zhang

Stochastic Processes and their Applications, 2025, vol. 188, issue C

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.

Keywords: Walsh diffusion; Multi-parameter process; Local time (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104672

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