Unbiased Function Simulation Based on Good Lattice Points

has no closed form and must be simulated, here by Quasi-Monte Carlo integration. Transformation to Periodicity on the Unit Cube: The periodicity of integrands in and on the unit cube plays an essential role in our solution. This is not a restrictive assumption however. With a change of variable, the domain of any function or the limits of any integral can be made the unit interval I or the unit cube. Similarly, any integrand on the unit cube, I, can be replaced by an integrand that is periodic with period 1 which has the same integral. For example, if, in (1.1), ( ) , k z θ is not periodic, apply the change in variable ( ) [ ] sin 2 ,0 1 2 t z t t t π φ π = = − ≤ ≤ (1.2)