2019/07/15 by Jasra, Ajay, Yu, Fangyuan, Heng, Jeremy · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)
paper · doi:10.48550/arxiv.1907.06328
In the following article we consider the numerical approximation of the non-linear filter in continuous-time, where the observations and signal follow diffusion processes. Given access to high-frequency, but discrete-time observations, we resort to a first order time discretization of the non-linear filter, followed by an Euler discretization of the signal dynamics. In order to approximate the associated discretized non-linear filter, one can use a particle filter (PF). Under assumptions, this can achieve a mean square error of O(ε2), for ε>0 arbitrary, such that the associated cost is O(ε-4). We prove, under assumptions, that the multilevel particle filter (MLPF) of Jasra et al (2017) can achieve a mean square error of O(ε2), for cost O(ε-3). This is supported by numerical simulations in several examples.