For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are designed to be computationally inexpensive, and much cheaper than exact library functions, and thus highly suitable for use in Monte Carlo simulations. Two approximations are presented for the Gaussian distribution: a piecewise constant on equally spaced intervals, and a piecewise linear using geometrically decaying intervals. The error of the approximations are bounded and the convergence demonstrated, and the computational savings measured for C and C++ implementations. Implementations tailored for Intel and Arm hardwares are inspected, alongside hardware agnostic implementations built using OpenMP. The savings are incorporated into a nested multilevel Monte Carlo framework with the Euler-Maruyama scheme to exploit the speed ups without losing accuracy, offering speed ups by a factor of 5--7. These ideas are empirically extended to the Milstein scheme, and the Cox-Ingersoll-Ross process' non central chi-squared distribution, which offer speed ups by a factor of 250 or more.

翻译：对于通过反向变换方法产生的随机变量,引入了近似随机变量,这些变量是按分布的反向累积分布函数近似值产生的。这些近似值设计为计算成本低,比精确的图书馆功能便宜得多,因此非常适合蒙特卡洛模拟使用。为高山分布提供了两种近似值:以平间距为平均间距的一个小数常数,以几何衰变间隔为计算线性线性。近似值的误差和显示的趋同,为C和C+++执行量测的计算节余。对专为英尔公司和Arm硬件设计的实施,以及使用 OpenMP 建造的硬件突触性实施都进行了检查。这些节约值被纳入了与Euler-Maruyama 计划一起的嵌入式多层蒙特卡洛框架,以便在不失去准确性的情况下利用速度上升,以5-7系数的速度上升。这些想法在经验上延伸至Milstein 方案,以及Cox-Ingersoll-Ros进程的非中央千位分布,以250或250倍的系数的速度上升。