Before revision:   This implies a reduction in cost compared to the (single level) EnKBF which requires a cost of O(\epsilon^{-3}) to achieve an MSE of O(\epsilon^2).
After revision:  In order to prove this result we provide a Monte Carlo convergence and approximation bounds associated to time-discretized EnKBFs. This implies a reduction in cost compared to the (single level) EnKBF which requires a cost of O(\epsilon^{-3}) to achieve an MSE of O(\epsilon^2).