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...
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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 |
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doaj-a7386204104b4035be71159e9d7ec3e92021-07-15T14:18:13ZengEDP 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Bencheikh O. Jourdain B. |
| 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 |
| author_facet |
Bencheikh O. Jourdain B. |
| author_sort |
Bencheikh O. |
| title |
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_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_sort |
bias behaviour and antithetic sampling in mean-field particle approximations of sdes nonlinear in the sense of mckean |
| publisher |
EDP Sciences |
| series |
ESAIM: Proceedings and Surveys |
| issn |
2267-3059 |
| publishDate |
2019-01-01 |
| 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. |
| url |
https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196509.pdf |
| work_keys_str_mv |
AT bencheikho biasbehaviourandantitheticsamplinginmeanfieldparticleapproximationsofsdesnonlinearinthesenseofmckean AT jourdainb biasbehaviourandantitheticsamplinginmeanfieldparticleapproximationsofsdesnonlinearinthesenseofmckean |
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1721300162196799488 |