Box-Muller Method for Normal (Gaussian) Deviates

* A Brief Introduction to Stochastic Differential Equations *

Box-Muller Method for Normal (Gaussian) Deviates

Normally distributed random numbers u are sampled from the density

$\begin{eqnarray} \frac{1}{\sqrt{2\pi }} e^{-u^2/2}.\nonumber \end{eqnarray}$

Such numbers can be numerically sampled from two uniform ([0, 1]) random numbers x₁ and x₂ through the formula

$\begin{eqnarray} y=\sqrt{-2\ln x_1}\cos (2\pi x_2).\nonumber \end{eqnarray}$

Random number generators for uniform random numbers are widely available.

* Innovative Stochastic Algorithms *