UNBIASED ESTIMATION OF THE VANILLA AND DETERMINISTIC ENSEMBLE KALMAN–BUCY FILTERS

In this paper, we consider the development of unbiased estimators for ensemble Kalman-Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology, which can be viewed as analog famous discrete-time Kalman filter. Our will motivated from recent work (Rhee and Glynn, Oper. Res., 63:1026-1053, 2015) introduces randomization means to produce finite variance estimators. enters through both level discretization number samples at each level. estimator specific models that are linear Gaussian. This due fact itself consistent, in large particle limit N → ∞, with filter, allows us one derive theoretical insights. Specifically, introduce two applied particular variants EnKBF, deterministic vanilla EnKBF. Numerical experiments conducted on Ornstein-Uhlenbeck process, includes high-dimensional example. compared multilevel. We also provide proof multilevel provides guideline some methods.