Abstract
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. 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 of Jasra et al. (SIAM J Numer Anal 55:3068–3096, 2017) can achieve a mean square error of O(ϵ2) , for cost O(ϵ- 3). This is supported by numerical simulations in several examples.
Original language | English (US) |
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Pages (from-to) | 1381-1402 |
Number of pages | 22 |
Journal | Statistics and Computing |
Volume | 30 |
Issue number | 5 |
DOIs | |
State | Published - Jun 17 2020 |
Bibliographical note
KAUST Repository Item: Exported on 2020-12-11Acknowledgements: AJ was supported by KAUST baseline funding. We thank two referees for comments that have greatly improved the article.