An efficient Monte Carlo scheme for Zakai equations
In this paper we develop a numerical method for efficiently approximating solutions of certain Zakai equations in high dimensions. The key idea is to transform a given Zakai SPDE into a PDE with random coefficients. We show that under suitable regularity assumptions on the coefficients of the Zakai...
| Príomhchruthaitheoirí: | , , , , |
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| Formáid: | Journal Article |
| Teanga: | English |
| Foilsithe / Cruthaithe: |
2024
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| Rochtain ar líne: | https://hdl.handle.net/10356/174134 |
| _version_ | 1826109485649756160 |
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| author | Beck, Christian Becker, Sebastian Cheridito, Patrick Jentzen, Arnulf Neufeld, Ariel |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Beck, Christian Becker, Sebastian Cheridito, Patrick Jentzen, Arnulf Neufeld, Ariel |
| author_sort | Beck, Christian |
| collection | NTU |
| description | In this paper we develop a numerical method for efficiently approximating solutions of certain Zakai equations in high dimensions. The key idea is to transform a given Zakai SPDE into a PDE with random coefficients. We show that under suitable regularity assumptions on the coefficients of the Zakai equation, the corresponding random PDE admits a solution random field which, for almost all realizations of the random coefficients, can be written as a classical solution of a linear parabolic PDE. This makes it possible to apply the Feynman–Kac formula to obtain an efficient Monte Carlo scheme for computing approximate solutions of Zakai equations. The approach achieves good results in up to 25 dimensions with fast run times. |
| first_indexed | 2024-10-01T02:18:58Z |
| format | Journal Article |
| id | ntu-10356/174134 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:18:58Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | ntu-10356/1741342024-03-18T15:35:11Z An efficient Monte Carlo scheme for Zakai equations Beck, Christian Becker, Sebastian Cheridito, Patrick Jentzen, Arnulf Neufeld, Ariel School of Physical and Mathematical Sciences Mathematical Sciences Zakai equation Nonlinear filtering problems In this paper we develop a numerical method for efficiently approximating solutions of certain Zakai equations in high dimensions. The key idea is to transform a given Zakai SPDE into a PDE with random coefficients. We show that under suitable regularity assumptions on the coefficients of the Zakai equation, the corresponding random PDE admits a solution random field which, for almost all realizations of the random coefficients, can be written as a classical solution of a linear parabolic PDE. This makes it possible to apply the Feynman–Kac formula to obtain an efficient Monte Carlo scheme for computing approximate solutions of Zakai equations. The approach achieves good results in up to 25 dimensions with fast run times. Nanyang Technological University Published version A.J. gratefully acknowledges the Cluster of Excellence EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation). A.N. acknowledges funding by the Nanyang Assistant Professorship Grant (NAP Grant) Machine Learning Based Algorithms in Finance and Insurance, Singapore. 2024-03-18T00:56:42Z 2024-03-18T00:56:42Z 2023 Journal Article Beck, C., Becker, S., Cheridito, P., Jentzen, A. & Neufeld, A. (2023). An efficient Monte Carlo scheme for Zakai equations. Communications in Nonlinear Science and Numerical Simulation, 126, 107438-. https://dx.doi.org/10.1016/j.cnsns.2023.107438 1007-5704 https://hdl.handle.net/10356/174134 10.1016/j.cnsns.2023.107438 2-s2.0-85168094285 126 107438 en Communications in Nonlinear Science and Numerical Simulation © 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). application/pdf |
| spellingShingle | Mathematical Sciences Zakai equation Nonlinear filtering problems Beck, Christian Becker, Sebastian Cheridito, Patrick Jentzen, Arnulf Neufeld, Ariel An efficient Monte Carlo scheme for Zakai equations |
| title | An efficient Monte Carlo scheme for Zakai equations |
| title_full | An efficient Monte Carlo scheme for Zakai equations |
| title_fullStr | An efficient Monte Carlo scheme for Zakai equations |
| title_full_unstemmed | An efficient Monte Carlo scheme for Zakai equations |
| title_short | An efficient Monte Carlo scheme for Zakai equations |
| title_sort | efficient monte carlo scheme for zakai equations |
| topic | Mathematical Sciences Zakai equation Nonlinear filtering problems |
| url | https://hdl.handle.net/10356/174134 |
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