Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean
In this paper, we prove that the weak error between a stochastic differential equation with nonlinearity in the sense of McKean given by moments and its approximation by the Euler discretization with time-step h of a system of N interacting particles is 𝒪(N-1+h). We provide numerical experiments con...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2019-01-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196509.pdf |
| _version_ | 1797965217142931456 |
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| author | Bencheikh O. Jourdain B. |
| author_facet | Bencheikh O. Jourdain B. |
| author_sort | Bencheikh O. |
| collection | DOAJ |
| description | In this paper, we prove that the weak error between a stochastic differential equation with nonlinearity in the sense of McKean given by moments and its approximation by the Euler discretization with time-step h of a system of N interacting particles is 𝒪(N-1+h). We provide numerical experiments confirming this behaviour and showing that it extends to more general mean-field interaction and study the efficiency of the antithetic sampling technique on the same examples. |
| first_indexed | 2024-04-11T01:56:32Z |
| format | Article |
| id | doaj.art-a7386204104b4035be71159e9d7ec3e9 |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T01:56:32Z |
| publishDate | 2019-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-a7386204104b4035be71159e9d7ec3e92023-01-03T05:13:32ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592019-01-016521923510.1051/proc/201965219proc196509Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKeanBencheikh O.Jourdain B.In this paper, we prove that the weak error between a stochastic differential equation with nonlinearity in the sense of McKean given by moments and its approximation by the Euler discretization with time-step h of a system of N interacting particles is 𝒪(N-1+h). We provide numerical experiments confirming this behaviour and showing that it extends to more general mean-field interaction and study the efficiency of the antithetic sampling technique on the same examples.https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196509.pdf |
| spellingShingle | Bencheikh O. Jourdain B. Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean ESAIM: Proceedings and Surveys |
| title | Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean |
| title_full | Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean |
| title_fullStr | Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean |
| title_full_unstemmed | Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean |
| title_short | Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean |
| title_sort | bias behaviour and antithetic sampling in mean field particle approximations of sdes nonlinear in the sense of mckean |
| url | https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196509.pdf |
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