In this paper, we study a numerical approximation scheme for reflected stochastic differential equations (SDEs) with non-Lipschitzian coefficients in a bounded convex domain. It is shown, under some mild conditions, that the approximation scheme converges in uniform \({{L}}^2 \) to the solution of reflected SDEs. Moreover, we move from local to global monotonicity conditions and consider the rate of convergence for our approximation scheme to reflected SDEs with coefficients which have at most polynomial growth.

中文翻译：

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具有非Lipschitzian系数的反射随机微分方程的一种逼近方案

在本文中，我们研究了在有界凸域中具有非李普希茨系数的反射随机微分方程 (SDE) 的数值逼近方案。结果表明，在一些温和的条件下，近似方案以均匀的\({{L}}^2 \)收敛到反射 SDE 的解。此外，我们从局部单调性条件转移到全局单调性条件，并考虑我们的近似方案的收敛速度，以反映具有最多多项式增长的系数的 SDE。