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|Title:||CONTRIBUTIONS TO MULTILEVEL AND MULTI-INDEX METHODS FOR PARTIALLY OBSERVED SYSTEMS||Authors:||XU YI||Keywords:||Multilevel Monte Carlo, Multi-index Monte Carlo, Sequential Monte Carlo, Partially Observed Deterministic System, Filtering, Smoothing||Issue Date:||7-Jun-2019||Citation:||XU YI (2019-06-07). CONTRIBUTIONS TO MULTILEVEL AND MULTI-INDEX METHODS FOR PARTIALLY OBSERVED SYSTEMS. ScholarBank@NUS Repository.||Abstract:||Practical problems which involve continuum fields have received a great deal of recent attention in the literature. The solutions to such continuum systems may not be solvable analytically. Typical computational issues arising from these systems is to approximate expectations of functional w.r.t. probability laws associated to the solutions to these continuum systems. One must resort to discretization methods before solving these systems numerically and the computation can be extremely challenging. In this thesis, we aim to reduce the associated cost to achieve a required level of error for computing expectations for such associated systems, by developing multilevel Monte Carlo (MLMC) and multi-index Monte Carlo (MIMC) algorithms.||URI:||https://scholarbank.nus.edu.sg/handle/10635/162444|
|Appears in Collections:||Ph.D Theses (Open)|
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