A GENERALIZATION OF WEYLS INTEGRATION THEOREM AND ITS MEANING FOR STOCHASTIC SIMULATIONS

Due to Weyl's integration theorem the Haar probability measure and, fu rther, a whole class of probability measures on a compact connected Li e group G can be represented as image measures of product measures of a specific type. It will be shown that this result holds even for a la rger class of probability measures on G. As a consequence, a simulatio n of any distribution which is contained in this (larger) class can be decomposed into two simulation problems of smaller size which can be treated independently. This aspect will be investigated and instructio ns will be worked out for applying the concept of decomposition in a c oncrete case. Their use and the benefit of the decomposition concept w ill be demonstrated at the special case G = SO(3).