Cylindrical Projections of Occupied Diffusions
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.
Cite
@article{arxiv.2604.25001,
title = {Cylindrical Projections of Occupied Diffusions},
author = {Valentin Tissot-Daguette and Xin Zhang},
journal= {arXiv preprint arXiv:2604.25001},
year = {2026}
}