Unbiased Estimation of the Vanilla and Deterministic Ensemble Kalman-Bucy Filters

@article{Alvarez2022UnbiasedEO,
  title={Unbiased Estimation of the Vanilla and Deterministic Ensemble Kalman-Bucy Filters},
  author={Miguel Alvarez and Neil K. Chada and Ajay Jasra},
  journal={ArXiv},
  year={2022},
  volume={abs/2208.03947}
}
In this article we consider the development of an unbiased estimator for the ensemble Kalman– Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology which can be viewed as a continuous-time analogue of the famous discrete-time ensemble Kalman filter. Our unbiased estimators will be motivated from recent work [Rhee & Glynn 2010, [31]] which introduces randomization as a means to produce unbiased and finite variance estimators. The randomization enters through both the level of… 

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