An algorithm for generating correlated random variables in a class of infinitely divisible distributions

A simple algorithm is proposed for generating a set of nonnegatively correlated variables having a specified correlation structure in a certain class of infinitely divisible distributions. These distributions are characterized by a property that they are closed under summation. The correlated Variables are expressed as sums of other independent random variables. The algorithm produces simple explicit expressions for typical correlation structures such as AR(1) correlation, banded correlation and symmetric correlation.