2023/02/20 by Ajay Jasra, Jasra, Ajay, Mohamed Maama +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Biology Tumor Growth #Numerical Analysis (math.NA) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2302.09978
openalex publication_date 2023/02/20 · openalex created_date 2023/12/15 · openalex updated_date 2026/07/28
In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which typically leads to filtering that is subject to discretization bias. The approach in [16] establishes that when only having access to the time-discretized diffusion it is possible to remove the discretization bias with an estimator of finite variance. We improve on the method in [16] by introducing a modified estimator based on the recent work of [17]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls.