  We present a new method for sampling the Levy area for a two-dimensional
Wiener process conditioned on its endpoints. An efficient sampler for the Levy
area is required to implement a strong Milstein numerical scheme to approximate
the solution of a stochastic differential equation driven by a two-dimensional
Wiener process whose diffusion vector fields do not commute. Our method is
simple and complementary to those of Gaines-Lyons and Wiktorsson, and amenable
to quasi-Monte--Carlo implementation. It is based on representing the Levy area
by an infinite weighted sum of independent Logistic random variables. We use
Chebychev polynomials to approximate the inverse distribution function of sums
of independent Logistic random variables in three characteristic regimes. The
error is controlled by the degree of the polynomials, we set the error to be
uniformly 10^(-12). We thus establish a strong almost-exact Levy area sampling
method. The complexity of our method is square logarithmic. We indicate how our
method can contribute to efficient sampling in higher dimensions.
