Walsh Spider Diffusions as Time Changed Multi-parameter Processes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866918068100268032 |
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| author | Bayraktar, Erhan Zhang, Jingjie Zhang, Xin |
| author_facet | Bayraktar, Erhan Zhang, Jingjie Zhang, Xin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_07101 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Walsh Spider Diffusions as Time Changed Multi-parameter Processes Bayraktar, Erhan Zhang, Jingjie Zhang, Xin Probability 60J60, 60G60 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. |
| title | Walsh Spider Diffusions as Time Changed Multi-parameter Processes |
| topic | Probability 60J60, 60G60 |
| url | https://arxiv.org/abs/2204.07101 |