In this work, we develop a multi-factor approximation for Stochastic Volterra Equations with Lipschitz coefficients and kernels of completely monotone type that may be singular. Our approach consists in truncating and then discretizing the integral defining the kernel, which corresponds to a classical Stochastic Differential Equation. We prove strong convergence results for this approximation. For the particular rough kernel case with Hurst parameter lying in $(0,1/2)$, we propose various discretization procedures and give their precise rates of convergence. We illustrate the efficiency of our approximation schemes with numerical tests for the rough Bergomi model.

中文翻译：

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具有完全单调型核的随机Volterra方程的逼近

在这项工作中，我们开发了具有Lipschitz系数和完全单调类型的核（可能是奇异的）的随机Volterra方程的多因子近似。我们的方法包括截断然后离散化定义内核的积分，该积分对应于经典的随机微分方程。我们证明了这种近似的强收敛性结果。对于Hurst参数在$（0,1 / 2）$中的特定粗糙核情况，我们提出了各种离散化程序，并给出了它们的精确收敛速度。我们通过对粗糙的Bergomi模型进行数值测试来说明近似方案的效率。