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arXiv · 1303.3717

Analysis of the Monte-Carlo error in a hybrid semi-lagrangian scheme

Charles-Edouard Bréhier·Erwan Faou
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Abstract

We consider Monte-Carlo discretizations of partial differential equations based on a combination of semi-lagrangian schemes and probabilistic representations of the solutions. We study the Monte-Carlo error in a simple case, and show that under an anti-CFL condition on the time-step $\delta t$ and on the mesh size $\delta x$ and for $N$ - the number of realizations - reasonably large, we control this error by a term of order $\mathcal{O}(\sqrt{\delta t /N})$. We also provide some numerical experiments to confirm the error estimate, and to expose some examples of equations which can be treated by the numerical method.

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Charles-Edouard Bréhier, Erwan Faou. 2013-03-15. Analysis of the Monte-Carlo error in a hybrid semi-lagrangian scheme. https://arxiv.org/abs/1303.3717

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