Cylindrical Projections of Occupied Diffusions

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.