Lecture 3 Pseudo-random number generation

We are going to apply this result for the case where A = [0, 1] 2
and f(x) = 1 for all x ∈ A (i.e. we start with a two-dimensional
uniformly distributed random variable) and choose the
transformation
x ↦→ h(x) =
�√−2 �
ln x1 cos(2πx2),
√
−2 ln x1 sin(2πx2).
The inverse of this transformation is given by
y ↦→ h −1 �
exp(−�y�
(y) =
2 �
/2),
arctan(y2/y1)/2π.
Computational Finance – p. 26