  Discrepancies play an important role in the study of uniformity properties of
point sets. Their probability distributions are a help in the analysis of the
efficiency of the Quasi Monte Carlo method of numerical integration, which uses
point sets that are distributed more uniformly than sets of independently
uniformly distributed random points. In this thesis, generating functions of
probability distributions of quadratic discrepancies are calculated using
techniques borrowed from quantum field theory.
  The second part of this manuscript deals with the application of the Monte
Carlo method to phase space integration, and in particular with an explicit
example of importance sampling. It concerns the integration of differential
cross sections of multi-parton QCD-processes, which contain the so-called
kinematical antenna pole structures. The algorithm is presented and compared
with RAMBO, showing a substantial reduction in computing time.
  In behalf of completeness of the thesis, short introductions to probability
theory, Feynman diagrams and the Monte Carlo method of numerical integration
are included.
