Cylindrical Projections of Occupied Diffusions

2026-04-27

AI Summary

This work addresses the computational intractability arising from infinite-dimensional occupation measure flows in path-dependent diffusion processes by introducing a cylindrical projection approximation framework, which effectively reduces the original system to a finite-dimensional dynamical system. The proposed method establishes, for the first time, rigorous theoretical guarantees for strong convergence along with explicit convergence rates, and further extends the analysis to weak error estimates. By integrating the Euler–Maruyama scheme with occupation measure theory, the framework enables efficient simulation of self-interacting diffusion processes. Its practical utility in financial derivative pricing is demonstrated through successful application to the Local Occupation Volatility (LOV) model, offering a novel tool for Monte Carlo simulation.

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.

Problem

• occupied diffusions
• infinite-dimensional
• computational intractability
• occupation measures
• path-dependent dynamics

Innovation

• cylindrical projections
• occupied diffusions
• strong convergence
• occupation measures
• Monte Carlo methods