  In this paper the computational aspects of probability calculations for
dynamical partial sum expressions are discussed. Such dynamical partial sum
expressions have many important applications, and examples are provided in the
fields of reliability, product quality assessment, and stochastic control.
While these probability calculations are ostensibly of a high dimension, and
consequently intractable in general, it is shown how a recursive integration
methodology can be implemented to obtain exact calculations as a series of
two-dimensional calculations. The computational aspects of the implementaion of
this methodology, with the adoption of Fast Fourier Transforms, are discussed.
