Iterative Particle Approximation for McKean-Vlasov SDEs with application to Multilevel Monte Carlo estimation

Understand

The mean field limits of systems of interacting diffusions (also called stochastic interacting particle systems (SIPS)) have been intensively studied since McKean \cite{mckean1966class}.

• The interacting diffusions pave a way to probabilistic representations for many important nonlinear/nonlocal PDEs, but provide a great challenge for Monte Carlo simulations.
• This is due to the nonlinear dependence of the bias on the statistical error arising through the approximation of the law of the process.
• This and the fact that particles/diffusions are not independent render classical variance reduction techniques not directly applicable and consequently make simulations of interacting diffusions prohibitive.