Multilevel particle filters for the non-linear filtering problem in continuous time
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2021-06-15
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ArticleAuthors
Jasra, Ajay
Yu, Fangyuan
Heng, Jeremy

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionStatistics
Date
2020-06-17Embargo End Date
2021-06-15Submitted Date
2019-07-15Permanent link to this record
http://hdl.handle.net/10754/660815
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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.Citation
Jasra, A., Yu, F., & Heng, J. (2020). Multilevel particle filters for the non-linear filtering problem in continuous time. Statistics and Computing, 30(5), 1381–1402. doi:10.1007/s11222-020-09951-9Sponsors
AJ was supported by KAUST baseline funding. We thank two referees for comments that have greatly improved the article.Publisher
Springer Science and Business Media LLCJournal
Statistics and ComputingarXiv
1907.06328Additional Links
http://link.springer.com/10.1007/s11222-020-09951-9ae974a485f413a2113503eed53cd6c53
10.1007/s11222-020-09951-9