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Semi-implicit Euler--Maruyama scheme for polynomial diffusions on the unit ball
Takuya Nakagawa, Dai Taguchi, Tomooki Yuasa · 2021-04-08 · via math.PR updates on arXiv.org

In this article, we consider numerical schemes for polynomial diffusions on the unit ball, which are solutions of stochastic differential equations with a diffusion coefficient of the form $\sqrt{1-|x|^{2}}$. We introduce a semi-implicit Euler--Maruyama scheme with the projection onto the unit ball and provide the $L^{2}$-rate of convergence. The main idea to consider the numerical scheme is the transformation argument introduced by Swart for proving the pathwise uniqueness for some stochastic differential equation with a non-Lipschitz diffusion coefficient.

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