Multilevel Ensemble Kalman–Bucy Filters

In this article we consider the linear filtering problem in continuous-time. We develop and apply multilevel Monte Carlo (MLMC) strategies for ensemble Kalman-Bucy filters (EnKBFs). These can be viewed as approximations of conditional McKean-Vlasov-type diffusion processes. They are also interpreted continuous-time analogue \textit{ensemble Kalman filter}, which has proven to successful due its applicability computational cost. prove that an ideal version our EnKBF achieve a mean square error (MSE) $\mathcal{O}(\epsilon^2), \ \epsilon>0$ with cost order $\mathcal{O}(\epsilon^{-2}\log(\epsilon)^2)$. result provide convergence approximation bounds associated time-discretized EnKBFs. This implies reduction compared (single level) requires $\mathcal{O}(\epsilon^{-3})$ MSE $\mathcal{O}(\epsilon^2)$. test theory on problem, motivate through high-dimensional examples $\sim \mathcal{O}(10^4)$ $\mathcal{O}(10^5)$.