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dc.contributor.authorBallesio, Marco
dc.contributor.authorJasra, Ajay
dc.contributor.authorvon Schwerin, Erik
dc.contributor.authorTempone, Raul
dc.date.accessioned2020-06-28T14:56:47Z
dc.date.available2020-06-28T14:56:47Z
dc.date.issued2020-04-09
dc.identifier.urihttp://hdl.handle.net/10754/663904
dc.description.abstractIn this paper, we consider the filtering problem for partially observed diffusions, which are regularly observed at discrete times. We are concerned with the case when one must resort to time-discretization of the diffusion process if the transition density is not available in an appropriate form. In such cases, one must resort to advanced numerical algorithms such as particle filters to consistently estimate the filter. It is also well known that the particle filter can be enhanced by considering hierarchies of discretizations and the multilevel Monte Carlo (MLMC) method, in the sense of reducing the computational effort to achieve a given mean square error (MSE). A variety of multilevel particle filters (MLPF) have been suggested in the literature, e.g., in Jasra et al., SIAM J, Numer. Anal.,55, 3068–3096. Here we introduce a new alternative that involves a resampling step based on the optimal Wasserstein coupling. We prove a central limit theorem (CLT) for the new method. On considering the asymptotic variance, we establish that in some scenarios, there is a reduction, relative to the approach in the aforementioned paper by Jasra et al., in computational effort to achieve a given MSE. These findings are confirmed in numerical examples. We also consider filtering diffusions with unstable dynamics; we empirically show that in such cases a change of measure technique seems to be required to maintain our findings.
dc.description.sponsorshipThis work is supported by the KAUST Office of Sponsored Research (OSR) under Award No.URF/1/2584-01-01 in the KAUST Competitive Research Grants Program-Round 4 (CRG2015) and the Alexander von Humboldt Foundation.
dc.publisherarXiv
dc.relation.urlhttps://arxiv.org/abs/2004.03981
dc.rightsArchived with thanks to arXiv
dc.subjectFiltering
dc.subjectDiffusions
dc.subjectMultilevel Monte Carlo
dc.subjectParticle Filters
dc.titleA Wasserstein Coupled Particle Filter for Multilevel Estimation
dc.typePreprint
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentStochastic Numerics Research Group
dc.eprint.versionPre-print
dc.contributor.institutionAlexander von Humboldt Professor in Mathematics for Uncertainty Quantification, RWTH Aachen University, Germany
dc.identifier.arxivid2004.03981
kaust.personBallesio, Marco
kaust.personBallesio, Marco
kaust.personJasra, Ajay
kaust.personvon Schwerin, Erik
kaust.personvon Schwerin, Erik
kaust.personTempone, Raul
kaust.personTempone, Raul
kaust.grant.numberURF/1/2584-01-01
refterms.dateFOA2020-06-28T14:56:47Z
kaust.acknowledged.supportUnitCompetitive Research
kaust.acknowledged.supportUnitOSR


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