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Walsh spider diffusions as time changed multi-parameter processes

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  • Bayraktar, Erhan
  • Zhang, Jingjie
  • Zhang, Xin

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.

Suggested Citation

  • Bayraktar, Erhan & Zhang, Jingjie & Zhang, Xin, 2025. "Walsh spider diffusions as time changed multi-parameter processes," Stochastic Processes and their Applications, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:spapps:v:188:y:2025:i:c:s0304414925001139
    DOI: 10.1016/j.spa.2025.104672
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    References listed on IDEAS

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    1. Karatzas, Ioannis & Yan, Minghan, 2019. "Semimartingales on rays, Walsh diffusions, and related problems of control and stopping," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 1921-1963.
    2. Bayraktar, Erhan & Zhang, Xin, 2021. "Embedding of Walsh Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 1-28.
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