Walsh Spider Diffusions as Time Changed Multi-parameter Processes
Probability
2025-06-24 v4
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
Cite
@article{arxiv.2204.07101,
title = {Walsh Spider Diffusions as Time Changed Multi-parameter Processes},
author = {Erhan Bayraktar and Jingjie Zhang and Xin Zhang},
journal= {arXiv preprint arXiv:2204.07101},
year = {2025}
}
Comments
Accepted by SPA