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arXiv · 1812.11932

Numerical methods for stochastic differential equations based on Gaussian mixture

Lei Li·Jianfeng Lu·Jonathan Mattingly·Lihan Wang
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Abstract

We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher order schemes for SDEs based on It\^o-Taylor expansion and iterated It\^o integrals, the proposed scheme approximates the probability measure $\mu(X^{n+1}|X^n=x_n)$ by a mixture of Gaussians. The solution at next time step $X^{n+1}$ is then drawn from the Gaussian mixture with complexity linear in the dimension $d$. This provides a new general strategy to construct efficient high weak order numerical schemes for SDEs.

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Lei Li, Jianfeng Lu, Jonathan Mattingly, Lihan Wang. 2018-12-31. Numerical methods for stochastic differential equations based on Gaussian mixture. https://doi.org/10.4310/cms.2021.v19.n6.a5

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