Walsh Spider Diffusions as Time Changed Multi-parameter Processes

2022/04/14 by Erhan Bayraktar, Bayraktar, Erhan, Jingjie Zhang +3
Decision Sciences · #60G60 #60J60 #Advanced Bandit Algorithms Research #Auction Theory and Applications #FOS: Mathematics #Game Theory and Applications #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2204.07101

openalex publication_date 2022/04/14 · openalex created_date 2022/04/19 · openalex updated_date 2026/07/28

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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