论文标题
近似逆累积分布函数以产生近似随机变量
Approximating inverse cumulative distribution functions to produce approximate random variables
论文作者
论文摘要
对于通过逆变换方法产生的随机变量，引入了近似随机变量，这些变量是通过分布的反向累积分布函数近似产生的。这些近似值设计为计算便宜，并且比精确的库函数便宜得多，因此非常适合用于蒙特卡洛模拟。为高斯分布提出了两个近似值：在间隔间隔的间隔间隔的分段常数，以及使用几何衰减间隔的分段线性。近似值的误差是有界的，并且展示了收敛性，并为C和C ++实现衡量了计算节省。检查了针对英特尔和手臂硬件量身定制的实现，并使用了使用OpenMP构建的硬件不可知论实现。节省的储蓄与Euler-Maruyama方案一起纳入了嵌套的多级蒙特卡洛框架中，以利用速度提高而不会失去准确性，从而使速度提高为5--7。这些想法在经验上扩展到了米尔斯坦计划，而Cox-ingersoll-ross过程的非中央卡方分布则提供了250倍或更高的速度。
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.
