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Cylindrical Projections of Occupied Diffusions

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  • Valentin Tissot-Daguette
  • Xin Zhang

Abstract

Occupied diffusions offer a Markovian framework for path-dependent dynamics by lifting the state space with a flow of occupation measures. Because this additional feature is infinite-dimensional, the simulation of these processes remains computationally intractable. We address this by introducing \textit{cylindrical projections}, which approximate the occupation flow via a finite-dimensional system. We establish the strong convergence of this approximation to the initial process and derive corresponding convergence rates. The method is validated through Euler--Maruyama simulations of self-interacting diffusions and an application to the Local Occupied Volatility (LOV) model in finance. Finally, we provide a weak error analysis and explore its consequences for Monte Carlo methods and derivatives pricing.

Suggested Citation

  • Valentin Tissot-Daguette & Xin Zhang, 2026. "Cylindrical Projections of Occupied Diffusions," Papers 2604.25001, arXiv.org, revised Jul 2026.
    • Handle: RePEc:arx:papers:2604.25001
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    References listed on IDEAS

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    1. Julien Guyon & Jordan Lekeufack, 2023. "Volatility is (mostly) path-dependent," Post-Print hal-04373380, HAL.
    2. Julien Guyon & Jordan Lekeufack, 2023. "Volatility is (mostly) path-dependent," Quantitative Finance, Taylor & Francis Journals, vol. 23(9), pages 1221-1258, September.
    3. Bruno Dupire, 2019. "Functional Itô calculus," Quantitative Finance, Taylor & Francis Journals, vol. 19(5), pages 721-729, May.
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    Cited by:

    1. Valentin Tissot-Daguette, 2026. "Pricing with Passion: The Local Occupied Volatility (LOV) Model," Papers 2604.26151, arXiv.org.
    2. Tissot-Daguette, Valentin, 2026. "Occupied processes: Going with the flow," Stochastic Processes and their Applications, Elsevier, vol. 195(C).

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