TY - JOUR

T1 - Multilevel particle filters for the non-linear filtering problem in continuous time

AU - Jasra, Ajay

AU - Yu, Fangyuan

AU - Heng, Jeremy

N1 - KAUST Repository Item: Exported on 2020-12-11
Acknowledgements: AJ was supported by KAUST baseline funding. We thank two referees for comments that have greatly improved the article.

PY - 2020/6/17

Y1 - 2020/6/17

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/660815

UR - http://link.springer.com/10.1007/s11222-020-09951-9

UR - http://www.scopus.com/inward/record.url?scp=85086864264&partnerID=8YFLogxK

U2 - 10.1007/s11222-020-09951-9

DO - 10.1007/s11222-020-09951-9

M3 - Article

VL - 30

SP - 1381

EP - 1402

JO - Statistics and Computing

JF - Statistics and Computing

SN - 1573-1375

IS - 5

ER -