Cylindrical Projections of Occupied Diffusions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911627829313536 |
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| author | Tissot-Daguette, Valentin Zhang, Xin |
| author_facet | Tissot-Daguette, Valentin Zhang, Xin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25001 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cylindrical Projections of Occupied Diffusions Tissot-Daguette, Valentin Zhang, Xin Numerical Analysis Probability Pricing of Securities 65C30, 60J25, 62C05, 65Z05 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. |
| title | Cylindrical Projections of Occupied Diffusions |
| topic | Numerical Analysis Probability Pricing of Securities 65C30, 60J25, 62C05, 65Z05 |
| url | https://arxiv.org/abs/2604.25001 |