Cylindrical Projections of Occupied Diffusions

Valentin Tissot-Daguette and Xin Zhang

Papers from arXiv.org

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.

Date: 2026-04
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