Log-normalization constant estimation using the ensemble Kalman–Bucy filter with application to high-dimensional models

Abstract In this article we consider the estimation of log-normalization constant associated to a class continuous-time filtering models. particular, ensemble Kalman–Bucy filter estimates based upon several nonlinear diffusions. Using new conditional bias results for mean aforementioned methods, analyze empirical log-scale normalization constants in terms their $\mathbb{L}_n$ -errors and -conditional bias. Depending on type diffusion, show that these are bounded above by such as $\mathsf{C}(n)\left[t^{1/2}/N^{1/2} + t/N\right]$ or $\mathsf{C}(n)/N^{1/2}$ ( -errors) $\mathsf{C}(n)\left[t+t^{1/2}\right]/N$ $\mathsf{C}(n)/N$ bias), where t is time horizon, N size, $\mathsf{C}(n)$ depends only n , not . Finally, use online static parameter models implement methodology both linear